Control method and system for solving two-dimensional coupling hydrodynamic model facing smart water conservancy

Abstract

The application discloses a one-dimensional and two-dimensional coupled hydrodynamic model solving control method and system for smart water conservancy, which sets a physical control plane and a degenerate accounting plane, and only sets a one-way passage from the physical control plane to the degenerate accounting plane; in a candidate trial process, every time the physical solution triggers a precision reduction correction, a measurement is written to a candidate counter in the degenerate accounting plane through the passage; after the candidate trial is completed, the candidate is pre-screened according to whether the physical report contains the precision reduction correction; the candidate that does not pass the pre-screening is discarded and disposed separately; the passed candidate is written into an official state array, and then the candidate counter is integrated into a total account and a step account and the candidate session is emptied; the physical control plane independently determines whether the solution continues to advance and when to terminate, and the degenerate accounting plane only receives one-way information. The application can separate the measurement of the precision reduction correction from the decision of the candidate in the solution process, and realizes fast, accurate and stable calculation.

Description

Technical Field

[0001] This invention relates to water conservancy informatization and computational hydrodynamics, and in particular to a one- or two-dimensional coupled hydrodynamic model solution and control method and system for smart water conservancy. Background Technology

[0002] The advancement of water conservancy informatization and the construction of digital twin river basins has gradually transformed hydrodynamic numerical models from offline analysis tools into computational kernels supporting online scheduling and real-time forecasting. In operations such as flood control scheduling, urban flooding simulation, and joint scheduling of reservoir groups, models must provide reliable results on the evolution of river floods and regional inundation processes within strict operational timeframes. Therefore, smart water conservancy projects three requirements that must be simultaneously met for one-dimensional and two-dimensional coupled hydrodynamic models: speed, accuracy, and stability. Speed ​​refers to completing the solution within the limited operational timeframe; accuracy means that the adopted hydrodynamic state accurately reflects the hydrodynamic control equations without carrying unidentified physical fidelity losses; stability means that calculations can continue under adverse conditions without the unbounded accumulation of physical fidelity losses.

[0003] One-dimensional and two-dimensional coupled hydrodynamic models are the core computational carriers for the aforementioned operations. The one-dimensional river network hydrodynamic model solves the one-dimensional Saint-Venant equations, characterizing the longitudinal flow evolution of the river channel and network; the two-dimensional floodplain hydrodynamic model solves the two-dimensional shallow water equations, characterizing the planar inundation process of floodplains, urban areas, and floodplains. These two models are coupled through lateral overflow exchange and estuary forward exchange to form a complete one-dimensional and two-dimensional coupled hydrodynamic model. Constrained by the Courant stability condition, the two-dimensional model requires very small time steps on fine-grid models, resulting in high computational costs for single simulations. In scenarios involving rolling updates of flood forecasts and multi-scheme ensemble simulations, the same physical process must be solved repeatedly, further amplifying the computational cost. Therefore, balancing solution speed, result accuracy, and computational stability in a parallel environment using a graphics processor has become a key challenge for the engineering application of this type of model.

[0004] To maintain computational continuity under adverse conditions such as wet-dry boundaries, steep hydraulic fronts, and ill-conditioned coupling interfaces, existing solvers generally apply protective numerical corrections during the numerical solution process. These corrections mainly include: limiting the volume fraction exceeding the limit or negative water depth to restore the unit water depth to non-negative; maintaining the state of units on the verge of drying up or degrading to prevent them from becoming unstable during updates; reducing the order of river segments dominated by local inertia to replace the complete momentum balance with a lower-order approximation; suppressing infeasible negative links to avoid non-physical backflow fluxes; and maintaining zero exchange at ill-conditioned coupling interfaces to suspend mass and momentum exchange between the first and second dimensions. While these corrections can maintain uninterrupted computation, they come at the cost of reducing the physical accuracy of the hydrodynamic equations. In essence, they sacrifice physical fidelity for numerical progress, and this application collectively refers to them as accuracy reduction corrections.

[0005] Existing technologies have the following shortcomings when handling accuracy reduction corrections:

[0006] First, the accuracy reduction correction is applied silently and not recorded during the solution process. A computational step that is numerically successful may have sacrificed physical fidelity. Users cannot distinguish whether the result of this step comes from the actual solution or from the protective correction. The adopted hydrodynamic state thus carries an invisible loss of physical fidelity, which contradicts the requirement of accurate calculation.

[0007] Secondly, several accounting and gating mechanisms introduced by the industry to constrain fidelity loss often result in the same ledger performing both measurement and adjudication functions. This ledger both counts the number of precision reduction corrections and, based on these counts, directly rejects candidate releases or terminates entire rounds of computation. This design, which combines measurement and control, means that if the ledger experiences measurement omissions, count overflows, or its own anomalies, it may mistakenly reject a candidate that should have been released, or even incorrectly terminate a solution that could have been continuously progressing. The reliability of the accounting mechanism thus becomes a hidden danger to the continuity of the solution, contradicting the requirement of stable computation.

[0008] Third, placing the accounting entries within the decision loop requires them to return a blocking status code and be read synchronously on the publishing path. In a massively parallel environment for graphics processors, such synchronous reads and global state accesses introduce implicit serialization between concurrent computing threads, significantly reducing parallel efficiency and contradicting the requirement for fast computation.

[0009] Fourth, the one-dimensional solution, two-dimensional solution, and coupled exchange modules each maintain inconsistent error correction logic, resulting in different handling of the same type of adverse working conditions. Furthermore, the coupling interface maintains duplicate entries for the same zero-exchange operation, leading to inconsistent behavior across modules and distorted attribution of fidelity loss. In summary, existing technologies lack a unified mechanism to simultaneously constrain these three requirements; achieving fast, accurate, and stable computation is difficult to coordinate and unify within the same framework. Summary of the Invention

[0010] Purpose of the invention: The purpose of this invention is to provide a one- or two-dimensional coupled hydrodynamic model solution control method and system for smart water conservancy that can separate the measurement of reduced accuracy correction from the decision of candidate release during the solution process, while meeting the requirements of calculation speed, result accuracy and calculation stability.

[0011] Technical Solution: The one-dimensional coupled hydrodynamic model solution control method for smart water conservancy described in this invention is used to control the candidate release of the formal state array of the one-dimensional river network solver, the two-dimensional flooding solver, and their coupled exchange pair in a parallel environment of a graphics processor, including:

[0012] Set up a physical control plane and a degenerate accounting plane, with only one unidirectional path between them from the physical control plane to the degenerate accounting plane;

[0013] During the current time step, candidate calculations are performed. During the candidate calculation process, each time the physical solution triggers a reduction in precision correction, a measurement is written to the candidate count in the degenerate accounting plane through this one-way path.

[0014] After the candidate calculations are completed, the candidates are pre-screened based on whether the physical report of this calculation includes a reduction in precision.

[0015] Candidates with reduced precision correction will be processed by the physical control plane as follows if they fail the pre-screening: reduce the time step and recalculate the candidate within the current time step, or keep it and advance the time with a strictly representable increment to make the floating-point time strictly monotonically increase, or terminate the operation.

[0016] Only candidates without downsizing correction are written to the formal state array, and after writing, the candidate count is merged into the general ledger and the step ledger, and the candidate count is cleared to zero at the same time;

[0017] The physical control plane determines whether the solution termination condition has been met. If not, it proceeds to the next time step and repeats the process of candidate trial calculation until the candidate count is entered into the general ledger.

[0018] The physical control plane independently determines whether the solution continues and when it terminates, while the degenerate accounting plane only receives one-way information from the physical control plane.

[0019] Structurally, the solution system is divided into two planes: the physical control plane and the degenerate ledger plane. A one-way path connects the two planes, from the physical control plane to the degenerate ledger plane, thus preventing the degenerate ledger plane from interfering with the physical solution from the information flow perspective. Regarding result accuracy, pre-screening is performed before candidates are written into the formal state array. Its criterion is whether the candidate's own physical report contains a reduction in precision correction, not the candidate count. Even if a candidate's trial calculation is numerically convergent, stable, and meets the physical tolerance criteria, it will not be written into the formal state array if its physical report contains a reduction in precision correction. Therefore, all candidates that can be written into the formal state array are those whose physical reports do not contain reduction in precision correction. The adopted formal states do not carry unidentified reduction in precision correction, ensuring result accuracy. Regarding computational stability, the pre-screening decision does not depend on the completeness of the candidate count; whether the candidate count is omitted or overflows does not change the pre-screening decision. The degenerate ledger plane only receives one-way information, and its measurement operations do not block the solution's progress. Whether the solution continues and when it terminates are determined independently by the physical control plane. Therefore, errors in the accounting mechanism will not interfere with the solution process, ensuring its stability. Regarding computational speed, since the degenerate accounting plane only receives unidirectional information, the physical control plane does not need to synchronously read the accounting status when performing candidate trials, pre-screening, and termination decisions, thus avoiding synchronous waiting caused by ledger access. This architecture allows for the full deployment of degenerate accounting on the host side in subsequent implementations, ensuring that parallel numerical computation on the graphics processing unit (GPU) side is not interrupted by accounting operations, thereby ensuring efficient computation. In summary, this method achieves accurate, stable, and fast computation through dual-plane separation and a unidirectional path.

[0020] Preferably, when the one-dimensional river network solver and the two-dimensional flooding solver are coupled for solving, the same candidate session is used. The coupling driver opens the candidate session, and this opening is idempotent. When the candidate session is open, there is no operation and the existing candidate count is retained. After the candidate session is opened, the one-dimensional solver and the two-dimensional solver only add the count to the candidate count within the candidate session. Before the one-dimensional and two-dimensional solution domains write the candidates without precision reduction corrections into the formal state array, all failure conditions are pre-checked so that the write operation only includes operations that have passed the check. After the pre-check, if the post-commit invariant of the one-dimensional solution domain is destroyed, it is judged to be unrecoverable and the operation is terminated. After both the one-dimensional and two-dimensional solution domains have completed the write operation, the coupling driver performs a candidate count merge into the ledger and clears the candidate session. The number of steps accepted by the coupling is always equal to the number of steps jointly submitted by the one-dimensional and two-dimensional solution domains.

[0021] By using the same candidate session and granting idempotency to the enable operation, the addition of metrics on the one-dimensional and two-dimensional sides within the same coupling step does not overwrite each other. Enabling on the two-dimensional side does not clear the metrics already written on the one-dimensional side, thus avoiding the problem of metric loss or attribution misalignment within the same coupling step. Pre-verification before the write operation ensures that the write operation in both domains only includes operations that have passed the verification. After the write is completed, the coupling driver uniformly executes the candidate count to be merged into the general ledger and the candidate session is cleared, ensuring that the candidate count calculation and session clearing in each step occur only once, avoiding duplicate or missed merging. As a result, the number of steps accepted by the coupling is always equal to the number of steps jointly submitted by the two domains, and the metric ledger maintains a strict correspondence with the physical progress of the coupling, providing a reliable foundation for ex-post auditing and accuracy traceability in coupled scenarios.

[0022] As a preferred approach, the criteria for determining whether a candidate contains a reduction in accuracy correction are determined based on the solution path: for two-dimensional solutions, the criteria are based on the actual physical changes in the physical report of the candidate trial calculation; for one-dimensional solutions, the criteria are based on whether the candidate triggers a preset disabled operator category; for coupled exchanges, the criteria are based on whether the candidate involves a pre-determined zero-exchange hold operation; writing the meter to the candidate count and performing pre-screening based on the physical report are executed independently.

[0023] The inclusion of precision reduction correction is determined by three specific criteria based on the solution path. This ensures that one-dimensional solutions, two-dimensional solutions, and coupled exchanges each employ identification methods consistent with their numerical characteristics, resolving inconsistencies in cross-module decision logic. Furthermore, writing metrology to candidate counts and pre-screening are executed independently. This means that the integrity of the metrology path is not a prerequisite for the correctness of pre-screening. Metering omissions in a particular solution path will not negatively impact candidate publication decisions through the pre-screening process, ensuring the stability of the solution process.

[0024] Preferably, the physical control plane is also equipped with a run identity lease that is isolated from the count in the degenerate accounting plane and is used to trigger the termination of the run. The run identity lease includes an occupant identifier and a run epoch. When dispatching across different solution types, if the occupant identifier or the run epoch does not match, the physical control plane will terminate the run.

[0025] By setting the runtime identity lease within the physical control plane, the identity verification function is assigned to the physical control plane, rather than being handled by the degenerate ledger plane. The runtime identity lease represents the complete identity of an active runtime using two parameters: the occupant identifier and the runtime epoch. When dispatching across different solution types, the physical control plane accurately identifies whether the current call still belongs to the same runtime at startup by comparing the occupant identifier and runtime epoch of the identity to be verified with that of the currently active identity. If a mismatch occurs between the occupant identifier or runtime epoch, it indicates that another concurrent runtime is attempting to perform an operation on the current formal state array. In this case, the physical control plane terminates the runtime, thus protecting the formal state array from being written only by the corresponding active runtime and preventing two concurrent runtimes from interfering with and polluting the formal state array. Because this lease is isolated from the counts in the degenerate ledger plane, the identity verification process neither reads any counts from the degenerate ledger plane nor is it affected by the plane's measurement results. Correspondingly, measurement operations in the degenerate ledger plane do not touch the runtime identity lease, further ensuring that the physical control plane and the degenerate ledger plane are independent and do not interfere with each other, ensuring computational stability.

[0026] As a preferred approach, the finiteness of the solution process is independently guaranteed by the physical control plane: each accepted time step and the floating-point time stored after each switch to hold increases strictly monotonically; the time step size has a positive lower limit, and when the time step size shrinks to the lower limit, it switches to hold or terminates the process; retry, substep, and iteration each have independent hard upper limits, and their counts do not overflow; the output and catch-up stages advance at a constant cost, and the cursor moves forward continuously with the processing progress.

[0027] The strict monotonically increasing and hold mechanism of floating-point time ensures that time progress will not stagnate; hard upper limits on retries, substeps, and iterations prevent unbounded retries; and the cursor continuously advances with the processing progress, preventing repeated replays. Together, these three elements ensure that even when degenerate accounting is completely uninvolved in control, the solution can be completed within a finite number of steps, maintaining or terminating, with bounded memory usage. The finiteness of the solution process is guaranteed from three dimensions: time progression, number of retries, and output catch-up. Moreover, these guarantees are all deployed within the physical control plane, independent of the degenerate accounting plane, ensuring stable solution progress.

[0028] Preferably, in the cell-by-cell and edge-by-edge kernel functions on the graphics processor device side, only numerical calculations and the setting of registration signals for unrecoverable errors and degradation registration signals are performed, and the device side only sends back these two types of signals to the host; degradation accounting and pre-screening are both performed on the host side; the unidirectional path is only performed on the host side.

[0029] By deploying degraded accounting and pre-screening judgments entirely on the host side, the device-side kernel function only retains numerical computation. This deployment prevents the device-side parallel threads from undertaking accounting and judgment tasks, avoiding memory access contention and implicit serialization introduced by ledger access in large-scale parallel threads. The device side only sends two types of signals back to the host, separating the deprecision correction measurement from the device-side numerical hot loop, allowing the parallel computing resources of the graphics processor to be concentrated on numerical solving, which is beneficial to improving the calculation speed.

[0030] As a preferred approach, when the degraded accounting plane encounters illegal categories, interface category mismatches, illegal weights, mismatched metering interface identities, write overflows, or failed audit evidence writing, it only accumulates evidence loss using a single summary count and marks the operation as incomplete evidence accordingly. The physical advancement and termination decisions for operations marked as incomplete evidence are still made independently by the physical control plane.

[0031] When situations such as illegal categories, interface category mismatches, identity mismatches, or write overflows occur during the measurement process, processing is not interrupted. Instead, all types of evidence losses are uniformly aggregated into a single summary count, and the audit integrity judgment is derived based on whether this count is zero. Thus, accounting anomalies are accurately reflected in the audit conclusions, rather than being transformed into interruption signals on the solution path. Physical progress and termination decisions are still made independently by the physical control plane, further confirming the isolation between accounting anomalies and physical solutions.

[0032] As a preferred approach, the degenerate accounting plane only performs a measurement function in the solution process; the progress results generated by the physical control plane have final effect; the system state transition is decided independently by the physical control plane; and the pre-screening determination is based solely on the physical reports of the candidates themselves.

[0033] Therefore, the degenerate accounting plane has no control over the solution process. The final effect of the physical progress results and the system state transitions belong to the physical control plane. The completeness of the accounting does not change any issued decisions.

[0034] As a preferred option, the degenerate accounting plane is carried out on a single process-level instance, and its state includes a running mode mirror, a candidate session open flag, a candidate count vector, a general ledger count vector, a step ledger count vector, and a summary count of evidence loss. The addition of each count adopts saturated addition operation. When it exceeds the maximum representable value of the integer used, it is recorded with saturated value and the evidence loss is accumulated through the summary count.

[0035] A single-process instance allows one-dimensional solvers, two-dimensional solvers, and coupled exchanges to share the same set of counting states, fundamentally avoiding inconsistencies in counting between multiple instances. Saturated addition ensures that the count remains within the integer representation range during accumulation, preventing exceptions or undefined behavior due to overflow. Overflow is preserved as an audit trail by summarizing the count and accumulating evidence loss. Thus, the stability of the degenerate accounting plane at the implementation level is guaranteed without interrupting physical progress.

[0036] The one- or two-dimensional coupled hydrodynamic model solution control system for smart water conservancy described in this invention is used to control the candidate release of the formal state array of the one-dimensional river network solver, the two-dimensional flooding solver, and their coupled exchange pair in a parallel environment of a graphics processor, including:

[0037] The physical control plane module is used to perform candidate trial calculations within the current time step. After the candidate trial calculations are completed, the candidates are pre-screened based on whether the physical report of this trial calculation contains a reduction in precision correction. If a candidate contains a reduction in precision correction, the physical control plane module will handle the candidate as follows if the candidate has not passed the pre-screening: reduce the time step and re-perform the candidate trial calculation within the current time step, or switch to holding and advance the time with a strictly representable increment to make the floating-point time strictly monotonically increase, or terminate the operation; only when the candidate does not contain a reduction in precision correction will the candidate be written into the formal state array, and after writing, the candidate count will be merged into the general ledger and the step ledger and the candidate count will be cleared to zero; and determine whether the solution termination condition has been met. If not, proceed to the next time step and repeat the above process.

[0038] The degenerate accounting plane module receives one-way information from the physical control plane module through a one-way path from the physical control plane module to the degenerate accounting plane module. During the candidate trial calculation process, each time the physical solution triggers a reduction in accuracy correction, a measurement is written to the candidate count in the degenerate accounting plane module through this one-way path.

[0039] The physical control plane module independently determines whether the solution should continue and when to terminate, while the degenerate accounting plane module only receives one-way information from the physical control plane module.

[0040] Beneficial effects: By dividing the solution system into a physical control plane and a degenerate accounting plane, and connecting the two with a one-way path, the decision-making power of pre-screening is fully retained in the physical control plane, while the degenerate accounting plane only undertakes the measurement function. Pre-screening is independent of measurement integrity to ensure accurate calculation, the finiteness of the solution is independently guaranteed by the physical control plane to ensure stable calculation, and accounting and pre-screening do not enter the device kernel function to ensure fast calculation. Attached Figure Description

[0041] Figure 1This is a schematic diagram of the overall process of the method of the present invention;

[0042] Figure 2 This is a schematic diagram of the dual-plane structure of the physical control plane and the degradation accounting plane, as well as the unidirectional path, of the present invention.

[0043] Figure 3 This is a schematic diagram of the candidate session lifecycle, operator measurement, and driver carryover process of the present invention.

[0044] Figure 4 This is a schematic diagram of the process for pre-screening and determining physical criteria based on the solution path in this invention;

[0045] Figure 5 This is a schematic diagram of the process of coupling the common synchronization and sharing candidate protocol and the driver transfer exactly once in this invention;

[0046] Figure 6 This is a schematic diagram of the accounting boundary between the host side and the device side of the graphics processor according to the present invention;

[0047] Figure 7 This is a flowchart illustrating the process of summarizing evidence loss and auditing completeness in this invention. Detailed Implementation

[0048] This invention will be further described in detail using a one-dimensional coupled hydrodynamic model as an example. This embodiment uses a one-dimensional river network hydrodynamic solver, a two-dimensional flooding hydrodynamic solver, and their coupled exchange to form a one-dimensional coupled hydrodynamic model. The two-dimensional solver solves in parallel on a graphics processor using a finite volume method. The system is divided into a physical control plane and a degradation accounting plane, with only one unidirectional path connecting them from the physical control plane to the degradation accounting plane. The overall structure is as follows: Figure 2 As shown. The physical control plane gathers all existing physical facilities and independently determines advancement and termination; the degradation accounting plane is a set of measurement states, carried by a single process-level instance.

[0049] First, the governing equations and candidate update forms are given, and then the solution control flow of this method is described in detail.

[0050] The one-dimensional river network hydrodynamic solver solves the conservation form of the one-dimensional Saint-Venant equations:

[0051] ,

[0052] ,

[0053] Where A is the cross-sectional area of ​​the water passage; Q is the cross-sectional flow rate; t represents the coordinates along the path; t represents time. denoted as lateral inflow per unit river length; g is the acceleration due to gravity; z is the free water surface elevation. The frictional gradient is used as the constant variable. This formula uses the cross-sectional flow rate as the conserved variable and the free water surface elevation gradient term to uniformly represent the pressure term and the bottom slope term. It is a commonly used conservation form for solving one-dimensional river networks.

[0054] A two-dimensional flood dynamics solver solves the conservation form of two-dimensional shallow water equations:

[0055] ,

[0056] ,

[0057] In the formula, is a vector of conserved variables; h is the water depth; x and y are two mutually orthogonal coordinates in the horizontal plane; and These represent the unit width flow rates in the x and y directions, respectively. and These are the flux vectors in the x and y directions, respectively; It is the source term vector containing the bottom slope and friction.

[0058] The two-dimensional solver advances at the control unit using a Godunov-type finite volume scheme, first obtaining the candidate element states and then using subsequent pre-screening to determine whether to write them into the final state:

[0059] ,

[0060] In the formula, This represents the candidate state of the i-th unit; Let be the formal state of the i-th unit at time level n; Δt is the time step. Let be the area of ​​the i-th unit; Let be the set of edges for the i-th unit; Let e ​​be the numerical flux obtained from the states on both sides of the edge, and let its two components correspond to the flux vectors in the x and y directions, respectively. and ; Let be the unit outward normal vector of edge e; Let be the numerical flux along the outer normal on edge e; Let e ​​be the length of edge e; This is the source item for the i-th unit. Candidate unit states must undergo pre-screening and adjudication before being written into the formal state array. This separation of candidate and formal update methods is the structural basis for the operator measurement and release control implemented in this invention: candidates carry physical change information awaiting adjudication, while formal states only carry state updates that have passed pre-screening and adjudication. In this invention, "candidate" refers to the candidate state.

[0061] like Figure 1The one- or two-dimensional coupled hydrodynamic model solution control method for smart water conservancy described in this invention includes:

[0062] Run identity lease and run reset:

[0063] Occupant identification in the physical control plane With the operating era Implement runtime identity leases. Each independent or coupled runtime occupies the lease at the starting point; if occupancy fails, it terminates. During dispatch across different solution types (i.e., the same runtime switching between one-dimensional solving, two-dimensional solving, and coupled exchange calls), the occupant of the currently active runtime is identified. With the operating era Make an identity matching determination:

[0064] ,

[0065] In the formula, The identifier of the occupant to be verified; The runtime epoch to be verified; and These are the identifier of the currently active occupier and the current operating era; This is an indicator function; it takes the value 1 if the condition inside the parentheses is true, and 0 if it is false. For logical AND operation. When In other words, when an identity mismatch occurs, the physical control plane terminates the run to prevent two concurrent runs from interfering with each other and polluting the formal state array. The run identity lease belongs to the physical control plane and is a data integrity component that can trigger run termination, isolated from the counts in the degenerate ledger plane. Each run start point simultaneously calls a run reset, clearing the general ledger count vector, step ledger count vector, candidate count vector, and evidence loss summary count to zero, and setting the candidate session open flag to false to ensure that the metering between different runs does not interfere with each other.

[0066] The degenerate accounting plane is initialized to a non-controlling accounting state:

[0067] The degenerate accounting plane is hosted on a single process-level instance, and its state includes a set of non-controlling accounting states: the runtime mirror (i.e., the runtime mode). (read-only image), candidate session open flag Candidate counting vector General ledger counting vector Step count vector Total count of evidence loss .in, In the physical control plane operation configuration, the operating mode is set to 1 for strict mode and 0 for derating mode. The degradation accounting plane only saves its mirror image for reporting; the pre-screening is used for... The runtime configuration is taken from the physical control plane; the runtime mode image of the degenerate accounting plane is not read, nor are any of the candidate count vectors, general ledger count vectors, step ledger count vectors, or evidence loss summary counts read; candidate session open flag. A value of 1 indicates that the candidate session is open, and a value of 0 indicates that it is not open; candidate session open flag. This flag is set and cleared by the corresponding driver in the physical control plane, and can be read back from the physical control plane. It is used to define the lifecycle of candidate sessions and the timing of self-checking shared candidate protocols on the coupling path. This flag does not carry any measurement; the determination of physical change indications and pre-screening indications does not involve any accounting status other than this flag. Candidate Count Vector The kth component Let k be the measure of the precision reduction correction of the k-th class in the current candidate session, where k is taken from the set of operator categories, and the total number of categories is denoted as K; the general ledger count vector. With step count vector Record the measurements carried over since the operation reset and in the current step respectively; record the total evidence loss count d, which records all evidence losses. All operations in the degenerate accounting plane always return to the normal status code, and never refuse to publish, stop progress, or roll back the committed physical state.

[0068] To ensure that addition does not produce exceptions or undefined behavior under any given value, all addition operations using the saturation addition operation are performed:

[0069] ,

[0070] in, The current value of the counter being incremented; For increments; The maximum representable value of the integer type used for this count. Exceed When saturation occurs, set This process records the loss of evidence, but never interrupts or rolls back the physical progress due to saturation. Thus, even in the extreme case of count overflow, the accounting plane adheres to the constraint of not disrupting the physical process.

[0071] Candidate Session Opening and Operator Metrics:

[0072] The lifecycle of a candidate session is as follows Figure 3 As shown, candidate sessions are opened by the corresponding drivers, and their opening is idempotent: when a candidate session is already opened (b = 1), the opening operation is null and the existing candidate count a is fully preserved; when not opened (b = 0), the count is set to zero. Meanwhile, 'a' retains its zero vector value after the previous clearing. This idempotency ensures that opening the two-dimensional side in the coupled solution does not clear the metrics already written on the one-dimensional side, which is a prerequisite for single-point accounting at the coupled interface. After the candidate session is opened, each time the physics triggers a reduction in precision belonging to the operator category, it writes a value to the candidate count with positive weight. After writing, it no longer reads the return value.

[0073] , ,

[0074] In the formula, The record weight for this correction is a positive integer; k is the operator category to which this correction belongs. If the submitted category is not an operator category, or the weight is not positive, or the attached occupant identifier and runtime epoch do not match the currently active runtime, then no count is written, and only a count is set. It will return a normal status code as usual, without interrupting physical progress. The operator metric is merely a mirror image of the physical decision; once written, it is not used as input for any published decision. Therefore, the presence or absence, or quantity, of the metric does not affect physical progress.

[0075] The main operator categories and their category codes included in this embodiment are shown in Table 1.

[0076] Table 1. Main operator categories, solution domains, and their econometric definitions

[0077]

[0078] Pre-screening:

[0079] Before any candidate state component is written into the formal state array, each candidate is pre-screened based on whether the physics report of this trial calculation contains a reduction in precision. The process of determining the judgment criteria according to the solution path is as follows: Figure 4 As shown. The authority of this pre-screening is the physical report of the candidate itself; candidate counts from the degraded accounting plane are prohibited from participating.

[0080] Let the physical change indication for this candidate trial be: This value is used to determine whether a candidate contains a reduction in precision correction. Its value is uniquely taken from the physical report of the trial calculation, that is, the repair flag or a similar physical change indication set in the physical report for the reduction in precision correction performed by the trial calculation.

[0081] ,

[0082] Where r is the pre-screening indicator, a value of 1 indicates rejection of the candidate posting, and a value of 0 indicates permission to post the candidate posting; This is the physical change instruction for this candidate, taken from the candidate's own physical report rather than the ledger count; m represents the operating mode, set to 1 in strict mode and 0 in derating mode. Physical Change Instruction The determination of the source is based on the solution path: For two-dimensional solutions, the actual physical changes in the physical report of the candidate trial are used as the basis for judgment, that is, whether the trial has applied a reduction in accuracy correction of the set repair flag; for one-dimensional solutions, the candidate is based on whether it has triggered the disabled operator category preset by the running mode; for coupled switching, the candidate is based on whether it involves a pre-determined zero-switching hold operation (that is, this path is constructed to propose a zero-switching hold path).

[0083] Since r is only The function is insensitive to any value of any component of the ledger candidate counting vector a:

[0084] , ,

[0085] In other words, the pre-screening decision is completely unrelated to whether the candidate count is complete or missing. Therefore, even if an operator metric in a certain solution path is missed, causing the candidate count to be affected... The underestimation is inconsistent with the physical judgment; the pre-screening should still be based on the physical judgment. It is the sole basis, and therefore its correctness does not depend on the completeness of any measurement, nor does it degenerate into a threshold comparison of ledger counts.

[0086] When r = 1, the candidate includes a precision reduction correction. Rejected candidates are not written into the formal state array and are discarded. The physical control plane handles them separately according to the category of the failure: failures that can be recovered by reducing the time step are recalculated within the current time step after reducing the time step size, with the number of retries subject to a hard upper limit; failures that can only be recovered by holding are converted to holding and the time is advanced with a strictly representable increment, making the floating-point time strictly monotonically increase; all other cases are judged as unrecoverable and the operation is terminated. The degenerate ledger plane neither generates alternative advancement results nor switches the backup solver, nor commands the system to enter any preset state based on ledger counts. The degenerate ledger plane only undertakes a measurement function in the solution advancement; the advancement results generated by the physical control plane have final effect, and the system state transition is decided independently by the physical control plane.

[0087] Write the formal state array and driver into the ledger:

[0088] When a candidate with r = 0 is approved for release, the candidate state is written to the official state array, thus completing the physical state commit (hereinafter referred to as commit). Subsequently, the corresponding driver merges the candidate count into the general ledger and step ledger in a saturation manner.

[0089] , , ,

[0090] in, For the general ledger count of category k; Count the steps for the kth class; For the k-th type of precision reduction, correct the candidate count within the current candidate session. Carry forward, that is, merge the candidate count into the general ledger and the step ledger (the same applies below). After completion, immediately clear the candidate session, i.e., set... and The carryover operation always occurs after the candidate state has been successfully written into the formal state array and the physical state has been submitted; if the candidate session is not open, the merge operation is a no-op. Even if the carryover process encounters a counter overflow, only the saturated value is used for merging. The system will never roll back committed physical states due to accounting overflow. If a physical validation fails before commit, the entire candidate state is discarded and the candidate session is cleared. Discarded candidates leave no trace in the official state array or the general ledger. Thus, the carry-over operation of the accounting plane strictly lags behind the physical commit. The fate of physical states is entirely decided by the physical control plane, and the accounting plane only performs post-event measurement, fundamentally eliminating the possibility of accounting interfering with physical states.

[0091] Summary of evidence loss and marking of incomplete evidence:

[0092] When encountering evidence loss situations such as illegal categories, interface category mismatches, illegal weights, mismatched measurement interface identities, write overflows, or failed audit evidence writing, the degraded accounting plane will not interrupt physical progress. Instead, it will only accumulate evidence loss using a single summary count d, and use this count to determine the audit integrity of the operation. Derived from:

[0093] ,

[0094] In the formula, For audit integrity indication, a value of 1 indicates audit integrity, and a value of 0 indicates incomplete evidence. That is, audit integrity is a derived judgment that the total evidence loss count equals zero, and is not stored separately. When d > 0, the run is marked as incomplete evidence; runs marked as incomplete evidence are not affected in their physical progression and termination, and the judgment is still made independently by the physical control plane, but are not considered audit integrity or certifiable release results. This mechanism completely isolates the anomalies of the accounting itself from the main solution path: anomalies are accurately recorded. Instead of introducing obstacles, this approach ensures that fidelity losses are perceptible rather than concealed, while guaranteeing that any anomalies in accounting records do not hinder the physical progress of the process. The process of summarizing evidence losses and the derived procedures for audit integrity are as follows: Figure 7 As shown.

[0095] Ensuring the activity of the physical control plane:

[0096] The finiteness of the solution process is independently guaranteed by the physical control plane and is independent of degradation accounting, including three guarantees.

[0097] First, time progresses strictly monotonically. Each accepted time step and the floating-point time stored after each transition to hold increases strictly monotonically, that is:

[0098] ,

[0099] The accepted time step has a positive lower bound:

[0100] ,

[0101] In the formula, For the j-th accepted time step or the floating-point time stored after being converted to hold; Let j be the time step size of the j-th accepted time step; This is the positive lower bound of the time step. When the time step has been reduced to the lower bound, the derating mode switches to hold and uses strictly representable increments. In strict mode, the advancement time is deemed unrecoverable and operation is terminated; when switching to hold mode, the strict increment must satisfy the following:

[0102] , ,

[0103] In the formula, fl(·) is a floating-point rounding operation; floating-point number The last unit is the difference between the floating-point number and its adjacent representable floating-point number. It is not less than the last unit, which ensures that the time advance of the holding step is not swallowed up by floating-point rounding.

[0104] Secondly, hard upper limits. Retry, substep and iteration are each given independent hard upper limits, and the derivation of their number is performed in a sufficiently wide integer or saturation manner to prevent the count from overflowing, thereby eliminating unbounded retries caused by count wrapping.

[0105] Third, output and catch-up operations proceed at a constant cost. The output and catch-up stages always advance at a constant cost; the cursor does not backtrack when a write operation fails, meaning the cursor continuously advances with the processing progress and there is no replay backlog, thus preventing input / output congestion caused by repeated replays. Therefore, the solution completes the advancement, holding, or termination within a finite number of steps, and the memory usage is bounded.

[0106] The physical control plane determines whether the solution termination condition has been met. If not, it proceeds to the next time step and repeats the process of candidate trial calculation until the candidate count is entered into the general ledger.

[0107] Graphics processor constraints:

[0108] In the two-dimensional solution, within the cell-by-cell and edge-by-edge parallel computation kernel function on the graphics processing unit (GPU) device side, calls to degenerate accounting and execution strategies are prohibited. That is, degenerate accounting and pre-screening are not performed within the kernel function. The device side only sends two types of signals back to the host: first, an unrecoverable error registration signal, with a sticky flag set for each type, triggering host-side termination; second, a degradation registration signal, with an idempotent sticky flag indicating that the device side applied a correction (keeping the physical quantity non-negative) or a limitation-type reduction in precision, without carrying the count or amplitude. The accounting boundary between the host side and the device side is as follows: Figure 6 As shown. After the kernel function returns and device synchronization is completed, within the time window before the candidate session is submitted or discarded, the host side drains the device flag once (i.e., reads the device-side sticky flag and then resets it, so that each trial calculation is consumed exactly once), and maps the degradation registration signal to an operator meter with unit weight and writes it into the candidate count, without distinguishing between rounding-level degradation and true-level degradation; if an unrecoverable error registration signal is received, termination is triggered.

[0109] Therefore, degenerate accounting and pre-screening are both executed on the host side at the running boundaries, step boundaries, candidate boundaries, and failure handling paths. Unidirectional paths do not enter the numerical hot loop or device kernel function execution; they are executed only on the host side. Replacing the hardware status flags of floating-point operations with discrete measurement on the host side, candidate-by-candidate, avoids both the implicit serialization inherent in the latter between concurrent floating-point instructions and the memory access contention caused by embedding accounting logic into massive parallel threads. This ensures that the solver's parallel computation on the GPU is not serialized by degenerate accounting.

[0110] Shared candidate sessions for coupled solutions:

[0111] In one-dimensional coupled operation, the one-dimensional solver, the two-dimensional solver, and the coupled exchange share the same candidate count and the same ledger within a single process-level instance. Coupled solving uses a single set of shared candidate counts, the protocol of which is as follows: Figure 5As shown, the sequence is fixed as follows: The coupling drive opens a candidate session at the start of the common step (i.e., the one-dimensional and two-dimensional solvers advance together within the same coupling time step, hereinafter referred to as the common step). This opening is idempotent; when a candidate session is open, it is an empty operation and retains the existing candidate count. After the candidate session is opened, the one-dimensional solver and the two-dimensional solver each only add metrics to the shared candidates within that candidate session, without carrying over or closing them. Before writing the candidates without precision reduction corrections into the formal state array in the one-dimensional and two-dimensional solution domains, all failure-prone conditions are pre-checked to ensure that the write operation only includes operations that have passed the check. After pre-checking, if the post-commit invariants of the one-dimensional solution domain are corrupted, it is judged as unrecoverable and the operation is terminated. The post-commit invariants refer to the invariants that are all failure-prone in both domains. After the failure condition has been pre-verified before writing and the two-dimensional solution domain has been written, the writing of the one-dimensional solution domain and its dependent conditions must be true and cannot fail. These conditions include the coupled transaction being active, the pre-verified acceptance time step being a finite positive value, the time advancement result obtained from this time step being representative and strictly increasing, and the state application of the one-dimensional final step being successful. If any of the above conditions are not met, it is immediately judged as an unrecoverable invariant violation, and the operation is terminated directly without entering the rollback recovery path. After both the one-dimensional and two-dimensional solution domains have completed the writing operation, the coupling driver performs exactly one carryover and closes the shared candidate, that is, performs exactly one candidate count and enters the general ledger and clears the candidate session. Any two-dimensional auxiliary process is prohibited from carrying over to one side of the coupled path.

[0112] Accordingly, the number of coupling steps accepted. The identity is equal to the number of steps jointly submitted by the one-dimensional solution domain and the two-dimensional solution domain. :

[0113] ,

[0114] In the formula, The number of steps for which coupling is accepted; This represents the number of steps required for the write operation to be completed jointly by the one-dimensional and two-dimensional solution domains.

[0115] This shared candidate protocol differs from two-phase commit protocols that use voting-based abort mechanisms, long-transaction methods that use compensation transaction rollback mechanisms, optimistic parallel discrete event simulations that use global virtual time commits and anti-message rollbacks for causal errors, and software fault-tolerant methods that use crash restarts instead of fault recovery: This protocol makes physical commits structurally unfailable by pre-verifying all possible failure conditions before committing, and does not use voting-based abort, compensation rollback, anti-message rollback, or crash restarts instead of recovery.

[0116] To illustrate the synergistic relationship of the above steps, two implementation examples are given below.

[0117] Example 1: Single-domain two-dimensional path. At the wet-dry dynamic boundary of a two-dimensional flooding example, a cell experiences a small negative water depth due to flux updates. The solver applies a volume fraction limit to this cell within the equipment-side kernel function to restore the water depth to non-negative and sets a degradation registration signal. This candidate step then numerically converges and stabilizes, satisfying the physically permissible criterion of non-negative water depth. During main-side drainage, this degradation registration signal is mapped to an operator meter of type CAT_2D_FRAC_CLAMP, written into the candidate count with unit weight, thus increasing the candidate count of this type. Add 1. In strict mode, the physics report for this candidate trial has the repair flag set, therefore the physics change indication... ,Depend on Knowing that the candidate contains a precision reduction correction, the candidate is not written into the official state array and is discarded; the physical control plane reduces the time step and recalculates the candidate within the current time step, with the number of retries subject to a hard upper limit; when the time step is reduced to the lower limit, it is considered unrecoverable and the operation is terminated. Even if operator metrics are omitted for any reason... No increase; pre-screening still due to The determination that the candidate includes a reduction in precision remains unchanged, demonstrating that the issuance of the ruling does not depend on the completeness of the measurement. Under the tolerance mode, Therefore Once a candidate is approved, it is written to the official status array (i.e., published). After the write is completed, the driver merges the candidate count into the general ledger, so that the current limit is counted in the general ledger count of the CAT_2D_FRAC_CLAMP class for post-event auditing.

[0118] Example 2 is implemented using a coupled solution path. The coupling driver opens a candidate session at the start of the common step. The one-dimensional zero-order final step (i.e., the final candidate step where the one-dimensional solution is completed in zero-order format in this step) triggers a forced zeroing belonging to the disabled operator category, adding a CAT_1D_FORCING_ZERO measure to the candidate count within the candidate session; on the two-dimensional side, a coupling zero-exchange hold is proposed at the ill-conditioned coupling interface, adding a CAT_COUPLED_ZERO_EXCHANGE_HOLD measure to the candidate count within the same candidate session. Since the candidate session is already open, the two-dimensional side's opening is a no-op and retains the measure already written on the one-dimensional side, thus the same fidelity loss event is not double-counted between the two domains. In strict mode, the physical change indication for the one-dimensional zero-order final step is taken from the physical determination of the disabled operator category, and the physical change indication for the coupling zero-exchange hold is taken from the zero-exchange hold operation predetermined for this path, i.e., the proposed operator intent is known for this path; both make... If a candidate is rejected and recalculated by reducing the time step size in the physical control plane, the process is terminated. When the time step size is reduced to the lower limit, the process is deemed unrecoverable and terminated. In derating mode, after both domains complete their physical submissions in a constructionally unfailable manner, the coupling driver performs a rollback, merging the shared candidate into the general ledger and closing the shared candidate. Coupling is accepted in this step if and only if both domains jointly submit; therefore, the number of accepted coupling steps is always equal to the number of steps jointly submitted by the one-dimensional and two-dimensional solution domains. Throughout the process, the running identity lease is verified using the occupant identifier and running epoch when dispatched across solution types. If the identities do not match, the run is terminated, while any operation on the degradation count does not interrupt the process.

[0119] As can be seen from the two implementation examples above, the present invention maintains the following consistent behavior regardless of whether it is a single-domain path or a coupled path: the pre-screening determination is uniquely derived from the physical determination and is independent of the ledger count; the accounting entry and pre-screening are executed independently; the merging into the general ledger is strictly delayed after the physical submission; and the coupled interface performs single-point accounting for the same event.

Claims

1. A solution control method for a one-dimensional coupled hydrodynamic model for smart water conservancy, used to control a one-dimensional river network solver, a two-dimensional flooding solver, and their coupled exchange pairs in a parallel environment of a graphics processor, for the candidate release of the formal state array, characterized in that, include: Set up a physical control plane and a degenerate accounting plane, with only one unidirectional path between them from the physical control plane to the degenerate accounting plane; During the current time step, candidate calculations are performed. During the candidate calculation process, each time the physical solution triggers a reduction in precision correction, a measurement is written to the candidate count in the degenerate accounting plane through this one-way path. After the candidate calculations are completed, the candidates are pre-screened based on whether the physical report of this calculation includes a reduction in precision. Candidates with reduced precision correction will be processed by the physical control plane as follows if they fail the pre-screening: reduce the time step and recalculate the candidate within the current time step, or keep it and advance the time with a strictly representable increment to make the floating-point time strictly monotonically increase, or terminate the operation. Only candidates without downsizing correction are written to the formal state array, and after writing, the candidate count is merged into the general ledger and the step ledger, and the candidate count is cleared to zero at the same time; The physical control plane determines whether the solution termination condition has been met. If not, it proceeds to the next time step and repeats the process of candidate trial calculation until the candidate count is entered into the general ledger. The physical control plane independently determines whether the solution continues and when it terminates, while the degenerate accounting plane only receives one-way information from the physical control plane.

2. The method according to claim 1, characterized in that, When the one-dimensional river network solver and the two-dimensional flooding solver are coupled to solve the problem, the same candidate session is used. The candidate session is opened by the coupling and the opening is idempotent. When the candidate session is already opened, there is no operation and the existing candidate count is retained. After a candidate session is opened, the one-dimensional solver and the two-dimensional solver each add a count to the candidate count within that session. Before writing the candidates without precision reduction corrections into the formal state array, both the one-dimensional and two-dimensional solver domains perform a pre-verification of all failure-prone conditions to ensure that the write operation only includes operations that have passed the verification. After the pre-verification, if the post-commit invariant of the one-dimensional solver domain is corrupted, it is considered unrecoverable and the process is terminated. After both the one-dimensional and two-dimensional solver domains have completed the write operation, the coupling driver performs a candidate count merge into the ledger and clears the candidate session. The number of steps accepted by the coupling is always equal to the number of steps jointly submitted by the one-dimensional and two-dimensional solver domains.

3. The method according to claim 1, characterized in that, The criteria for determining whether a candidate contains a reduction in accuracy correction are determined by source according to the solution path: for two-dimensional solutions, the actual physical changes in the physical report of the candidate trial calculation are used as the basis; for one-dimensional solutions, whether the candidate triggers a preset disabled operator category is used as the basis; for coupled exchanges, whether the candidate involves a pre-determined zero-exchange hold operation is used as the basis; writing the meter to the candidate count and pre-screening based on the physical report are performed independently.

4. The method according to claim 1, characterized in that, The physical control plane also includes run identity leases that are isolated from the counts in the degenerate accounting plane and are used to trigger the termination of the run. The run identity lease includes the occupant identifier and the run epoch. When dispatching across different solution types, if the occupant identifier or the run epoch does not match, the physical control plane will terminate the run.

5. The method according to claim 1, characterized in that, The finiteness of the solution process is independently guaranteed by the physical control plane: each accepted time step and the floating-point time stored after each switch to hold increases strictly monotonically; the time step size has a positive lower limit, and when the time step size shrinks to the lower limit, it switches to hold or terminates the process; retry, substep and iteration each have independent hard upper limits, and their counts do not overflow; the output and catch-up links advance at a constant cost, and the cursor moves forward continuously with the processing progress.

6. The method according to claim 1, characterized in that, Within the cell-by-cell and edge-by-edge kernel functions on the graphics processor device side, only numerical calculations and the setting of registration signals for unrecoverable errors and degradation registration signals are performed. The device side only sends back these two types of signals to the host. Degradation accounting and pre-screening are both performed on the host side. The unidirectional path is performed only on the host side.

7. The method according to claim 1, characterized in that, When the degraded accounting plane encounters illegal categories, interface category mismatches, illegal weights, mismatched metering interface identities, write overflows, or failed audit evidence writing, it only accumulates evidence loss using a single summary count and marks the operation as incomplete evidence. The physical advancement and termination decisions for operations marked as incomplete evidence are still made independently by the physical control plane.

8. The method according to claim 1, characterized in that, The degenerate accounting plane only performs a measurement function in the solution process; the progress results generated by the physical control plane have final effect; system state transitions are decided independently by the physical control plane; the pre-screening judgment is based solely on the physical reports of the candidates themselves.

9. The method according to claim 1, characterized in that, The degenerate accounting plane is carried out on a single process-level instance. Its state includes the running mode mirror, candidate session open flag, candidate count vector, general ledger count vector, step ledger count vector, and evidence loss summary count. The addition of each count adopts saturated addition operation. When it exceeds the maximum representable value of the integer used, it is recorded with saturated value and evidence loss is accumulated through summary count.

10. A one- or two-dimensional coupled hydrodynamic model solution control system for smart water conservancy, used to control a one-dimensional river network solver, a two-dimensional flooding solver, and their coupled exchange pairs for candidate release of formal state arrays in a graphics processor parallel environment, characterized in that... include: The physical control plane module is used to perform candidate trial calculations within the current time step; After the candidate trial calculation is completed, the candidates are pre-screened based on whether the physical report of this trial calculation contains a reduction in precision correction. If the candidate contains a reduction in precision correction, the physical control plane module will handle the candidate as follows if the candidate fails the pre-screening: reduce the time step and re-perform the candidate trial calculation in the current time step, or switch to holding and advance the time with a strictly representable increment to make the floating-point time strictly monotonically increase, or terminate the operation; only if the candidate does not contain a reduction in precision correction, the candidate is written to the formal state array, and after writing, the candidate count is merged into the general ledger and the step ledger and the candidate count is cleared to zero; and it is determined whether the solution termination condition has been met. If not, the process proceeds to the next time step and repeats the above process. The degenerate accounting plane module receives one-way information from the physical control plane module through a one-way path from the physical control plane module to the degenerate accounting plane module. During the candidate trial calculation process, each time the physical solution triggers a reduction in accuracy correction, a measurement is written to the candidate count in the degenerate accounting plane module through this one-way path. The physical control plane module independently determines whether the solution should continue and when to terminate, while the degenerate accounting plane module only receives one-way information from the physical control plane module.

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