A simulation optimization design method of a GPU liquid cooling plate, electronic equipment and storage medium
By setting up independent parallel paths in the GPU liquid cooler and combining them with the pre-allocation of flow rates based on weight and cooling amount, along with three-dimensional computational fluid dynamics simulation and filtering optimization algorithms, precise heat dissipation matching for each heat-generating area of the GPU is achieved. This solves the problem of uneven cooling flow distribution in existing technologies and improves the balance between heat dissipation efficiency and flow resistance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TIANHE SUPERCOMPUTING HUAIHAI SUB CENT
- Filing Date
- 2026-05-25
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies fail to effectively differentiate the cooling flow based on the specific cooling requirements of each heat-generating area of the GPU, and fail to combine efficient parametric modeling and iterative optimization strategies to achieve rapid and precise customization of liquid cooling plate structures, especially in cases of uneven heat distribution in the GPU.
By constructing a liquid-cooled plate flow channel structure, setting up independent parallel paths corresponding to the heating areas, and pre-allocating the flow rate by combining the weight of each area with the cooling amount, a three-dimensional computational fluid dynamics simulation model is established. A filtering optimization algorithm is used to iteratively optimize the horizontal side length of each path to meet the temperature deviation requirements.
It achieves precise matching of cooling resources with the heat dissipation needs of different heat-generating areas such as GPU chips and memory, avoiding energy waste caused by the global uniform adjustment of flow in traditional solutions, and effectively balancing heat dissipation efficiency and flow resistance.
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Figure CN122242393A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of heat dissipation technology for electronic devices, and in particular to a simulation optimization design method for a GPU liquid cooler, an electronic device, and a storage medium. Background Technology
[0002] With the rapid development of artificial intelligence technology, the global demand for graphics processing units (GPUs) has increased dramatically, leading to significant performance improvements and a significantly faster iteration speed for GPU products. This trend has directly resulted in a corresponding increase in the demand for GPU liquid cooling plates, requiring rapid iteration in their structural designs. For the liquid cooling plate manufacturing industry, providing customized liquid cooling plate structural designs for different GPU models and application scenarios, and being able to efficiently and effectively complete the simultaneous R&D of matching liquid cooling plates before the launch of next-generation GPU products, has become crucial for enhancing companies' market competitiveness.
[0003] In diverse application scenarios such as graphics rendering, artificial intelligence computing, and scientific data analysis, supercomputing centers and enterprises are increasingly inclined to deploy customized GPU computing clusters to achieve deep optimization for specific task scenarios. In this context, GPU heat dissipation strategies must be closely optimized around specific task scenarios, and the heat dissipation structure of liquid cooling plates also needs corresponding adjustments. Furthermore, the heat generation of different areas of a GPU varies significantly during operation; for example, the chip is the core heat-generating area, followed by the memory, while other areas generate relatively less heat. Therefore, an ideal liquid cooling plate solution should be able to achieve targeted heat dissipation, concentrating the main cooling resources on the core heat-generating areas to avoid energy waste.
[0004] In the prior art, there are already design methods for cold plate flow channels targeting non-uniform heat distribution. For example, patent document CN115017639B discloses a method that constructs a two-dimensional topology optimization model and performs iterative calculations with the goal of minimizing fluid power dissipation and maximizing heat transfer using a weighted function, ultimately obtaining the cold plate flow channel structure. This method achieves the adaptability of the flow channel structure to non-uniform heat distribution by setting a heat distribution coefficient related to the heat distribution form of the heat source. Another patent document CN117494335A discloses a topology optimization design method for a heat dissipation cold plate structure for non-uniform heat sources. It projects the topology optimization region and the non-topology optimization region onto the substrate to generate a double-layer coupled planar model, and introduces the RAMP function for interpolation. It performs topology optimization to minimize the pressure difference and obtains the fin profile structure.
[0005] The aforementioned existing technologies all achieve flow channel or fin structures adapted to non-uniform heat sources through topology optimization methods, but their optimization objectives mainly focus on balancing flow power consumption and heat transfer or minimizing pressure drop. However, existing technologies do not fully consider how to pre-allocate cooling flow rates according to the specific cooling requirements of various heat-generating areas of the GPU (such as chips and memory) during the liquid cooler design process, and how to use this as a basis, combined with efficient parametric modeling and iterative optimization strategies, to achieve rapid and accurate customization of the liquid cooler structure (especially the flow channel cross-sectional dimensions). Furthermore, how to effectively utilize historical simulation data and improve optimization efficiency and accuracy during the structural optimization process is also rarely addressed in existing technologies. Summary of the Invention
[0006] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows: According to a first aspect of the present invention, a simulation optimization design method for a GPU liquid cooler is provided, the method comprising the following steps: S100, determine n heat-generating areas of the GPU and the preset temperature expectation value and cooling amount of each heat-generating area, wherein the cooling amount is determined based on the difference between the operating temperature of the heat-generating area and the preset temperature expectation value.
[0007] S200, construct a liquid cooling plate flow channel structure, the liquid cooling plate flow channel structure includes an inlet, an outlet and n parallel channels connecting the inlet and the outlet, each channel having different horizontal side lengths and corresponding to a heating area.
[0008] S300, the total flow rate flowing into the inlet is pre-allocated into flow rates flowing into n sub-channels respectively. The sub-channels correspond one-to-one with the main channel. The flow rate allocation ratio of each sub-channel is set according to the weight of the corresponding heating area and / or the cooling amount.
[0009] S400, establish a three-dimensional computational fluid dynamics simulation model that includes the liquid cooling plate flow channel structure and the GPU structure.
[0010] S500 uses the horizontal side length of each passage as the optimization variable, and aims to satisfy a preset condition by ensuring that the deviation of the simulated temperature monitoring value of each heating region from the preset expected temperature value meets the preset condition. The optimization variables are substituted into the three-dimensional computational fluid dynamics simulation model, and a filtering-type optimization algorithm is used for iterative optimization until an optimization result satisfying the preset condition is obtained. (Rectangular cross-section) According to a second aspect of the present invention, an electronic device is provided, including a processor and a memory; the processor executes the steps of the method described in the first aspect of the present invention by invoking a program or instructions stored in the memory.
[0011] According to a third aspect of the present invention, a computer-readable storage medium is provided that stores a program or instructions that cause a computer to perform the steps of the method described in the first aspect of the present invention.
[0012] The present invention has at least the following beneficial effects: This invention achieves precise matching of cooling resources with the heat dissipation needs of different heat-generating areas such as GPU chips and memory by setting independent parallel paths corresponding to each heat-generating area and pre-allocating flow based on the weight of each area and the amount of cooling. This avoids the energy waste caused by the global uniform adjustment of flow in traditional solutions. Through filter-type optimization iteration with the cross-sectional size of each path as the optimization variable and the temperature deviation as the constraint, the synergistic optimization of the flow channel structure and flow distribution is achieved, effectively balancing heat dissipation efficiency and flow resistance.
[0013] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 A flowchart illustrating a simulation optimization design method for a GPU liquid cooler provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a liquid cooling plate structure. Detailed Implementation
[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0017] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.
[0018] It should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. A process can be terminated when its operation is complete, but it may also have additional steps not included in the figures. A process can correspond to a method, function, procedure, subroutine, subroutine, etc.
[0019] This invention is primarily applied to the field of GPU (Graphics Processing Unit) heat dissipation, particularly liquid cooling systems for high-performance GPUs in data centers, supercomputing centers, and artificial intelligence computing clusters. With the rapid development of artificial intelligence technology, the demand for GPU computing power has increased dramatically, leading to a significant rise in power consumption and heat generation. Traditional air cooling is no longer sufficient to meet the heat dissipation needs of high-power GPUs, and liquid cooling is gradually becoming the mainstream solution.
[0020] The workload characteristics of GPUs vary significantly across different application scenarios: in AI training scenarios, GPUs operate at full load for extended periods, resulting in persistently high temperatures in both the chip and memory areas; in graphics rendering scenarios, GPU load fluctuates considerably, with heat generation in different areas changing dynamically over time; and in scientific computing scenarios, GPUs may experience intermittent high loads. These differences necessitate different customization requirements for the flow distribution and channel layout of liquid coolers.
[0021] In addition, the pace of GPU product iteration is accelerating. Before the next generation of GPUs is launched, it is necessary to develop a matching liquid cooling plate. Traditional design methods that rely on experience are time-consuming and inefficient, making it difficult to meet the demand for rapid market launch.
[0022] This invention provides a simulation optimization design method for liquid coolers for GPUs, which can quickly customize and design a liquid cooler structure with reasonable flow distribution and optimized flow channel layout based on the actual heat characteristics, workload mode and heat dissipation requirements of the GPU, so as to meet the heat dissipation requirements of different application scenarios and shorten the research and development cycle.
[0023] like Figure 1 As shown, the method includes the following steps: S100 determines the n heat-generating areas of the GPU and the preset temperature expectation and cooling amount for each heat-generating area.
[0024] This step first identifies the heat-generating areas of the GPU that require cooling under stable operating conditions. Based on the actual operating characteristics of the GPU, its main heat-generating areas include the chip area and the memory area, with other areas (such as the power supply module and interface circuits) considered as other heat-generating areas. In this embodiment, the GPU is the target GPU for which the liquid cooling plate to be designed needs to dissipate heat.
[0025] To facilitate differentiated flow allocation based on the cooling needs of different heat-generating areas, this step divides the n heat-generating areas into a first type and a second type. The first type refers to areas where cooling capacity needs dynamic adjustment when the workload changes; the heat generated in these areas fluctuates significantly with changes in GPU computing load, and their cooling requirements are time-varying and uncertain. The second type refers to areas where cooling requirements remain relatively stable when the workload changes; the heat generated in these areas fluctuates less under different operating conditions, and their cooling requirements are relatively constant.
[0026] Specifically, suppose there are n heat-generating areas that need heat dissipation (n≥2), labeled as area 1 to area n respectively. For example... Figure 2 As shown in the illustration, this embodiment schematically depicts five heating areas, namely heating areas HA1 to HA5. Wherein: The heat-generating area HA1 is the GPU chip area, which belongs to the first type of heat-generating area; The heat-generating region HA2 is the memory region and belongs to the first type of heat-generating region. Fever areas HA3 to HA5 are other fever areas, belonging to the second category of fever areas.
[0027] To accurately reflect the heat dissipation requirements of each heat-generating area under different operating conditions, this embodiment uses the following method to determine the operating temperature of each area: For the first type of heat-generating area (chip area and memory area), since it operates under two typical conditions in actual operation—low load and full load—and the operating temperature under low load is closer to its basic heat dissipation requirements, the average temperature under stable low load operation is taken as the operating temperature. Let the operating temperature of the chip area be T. 1 w The operating temperature of the memory region is T. 2 w .
[0028] For the second type of heat-generating area (other heat-generating areas), since its heat generation is relatively stable and fluctuates little under different operating conditions, its average temperature under stable full-load operation is taken as the operating temperature. Let the operating temperature of the other areas be T. i w , where i=3,……,n.
[0029] Each heating zone has a preset desired temperature value, denoted as T. j c , j=1, ..., n. This expected temperature value can be preset according to the specifications of the GPU chip, system thermal design parameters, or user needs.
[0030] The cooling amount of each heating zone is defined as the difference between the operating temperature and the expected temperature of that heating zone, i.e.: △T j =T j w -T j c .
[0031] Among them, △T j This represents the cooling amount for the j-th heat-generating region. Its value reflects the heat dissipation intensity required for that region, and a larger value indicates that more cooling resources are needed.
[0032] Based on the above classification, when pre-allocating the total flow in the subsequent step S300, the flow allocated to the path corresponding to the first type of heat-generating area and the flow allocated to the path corresponding to the second type of heat-generating area are adjusted independently to achieve dynamic response and precise resource allocation for the core heat-generating area.
[0033] S200, constructing a liquid cooling plate flow channel structure.
[0034] Based on the number and classification of heat-generating areas determined in step S100, this step constructs a matching liquid cooling plate flow channel structure.
[0035] Specifically, such as Figure 2 As shown, the liquid-cooled plate flow channel structure 1 includes an inlet 2, an outlet 3, and n parallel channels connecting the inlet and the outlet. Each channel has a rectangular cross-section (including rectangles, squares, etc.), and the n channels correspond one-to-one with the n heat-generating areas determined in step S100, each used for independent heat dissipation of its respective heat-generating area. As an example, Figure 2 The diagram shows five heating zones HA1 to HA5, and correspondingly, the liquid cooling plate flow channel structure 1 includes five parallel channels. In this embodiment, the rectangular cross-section is preferably rectangular.
[0036] In terms of flow channel cross-section design, this embodiment adopts the following method to achieve a parallel layout of multiple channels. Taking the liquid cooling plate substrate plane as a reference, the direction perpendicular to the substrate is the vertical direction, and the direction parallel to the substrate is the horizontal direction. Let the overall cross-section of the flow channel be rectangular, with the vertical side length denoted as 'a' and the horizontal side length as 'b'. During manufacturing, the vertical side length 'a' remains constant, and the horizontal direction is divided by a wall thickness 'c', forming n parallel independent channels, where the wall thickness 'c' is much smaller than the horizontal side length 'b'. Each channel has an independent rectangular cross-section, with its horizontal side length denoted as 'b'. j Then the cross-sectional area of each path is a·b j The horizontal side lengths of each channel are different, meaning they are all different from each other. Their specific values are set differently according to the heat dissipation requirements (such as cooling amount) of each heat-generating area. The larger the value, the larger the flow cross-sectional area of the channel, and the greater the flow rate it can carry.
[0037] To complement the pre-allocation of total flow rate in step S300, a main channel is established after the inlet. This main channel is divided into n sub-channels, each corresponding to a specific path. Each sub-channel receives the pre-allocated flow rate from step S300 and independently inputs this flow rate into its corresponding path. After the n paths have completed heat dissipation in their respective heat-generating areas, they finally converge and flow out at the outlet.
[0038] Furthermore, to further improve heat dissipation efficiency, the shape of the rotation path of each channel within its corresponding heat-generating area can be customized according to the planar geometry of that heat-generating area. Specifically, for heat-generating areas with irregular shapes or uneven local heat flux density distribution, the rotation method of the channel (such as bending angle, number of rotations, flow channel density, etc.) can be adjusted accordingly to spatially match the flow channel layout with the geometric contour and heat distribution characteristics of the heat-generating area, thereby optimizing the convective heat transfer effect.
[0039] Based on the above flow channel structure, the effective heat dissipation capacity of each channel can be evaluated using heat transfer theory. Assuming the effective cooling length of each channel is L, then the convective heat transfer area of each channel is 2·(a+b) / 2. j (Considering the four sidewalls of the rectangular cross-section, ignoring the influence of the inlet and outlet at both ends). Therefore, the heat dissipation capacity of a single passage can be expressed as: Φ j =2·(a+b j )·L·h·△T.
[0040] Where h is the convective heat transfer coefficient, and ΔT is the temperature difference between the wall and the fluid. This theoretical relationship provides a physical basis for optimizing the horizontal side length of each passage in the subsequent step S500, that is, increasing the horizontal side length can increase the heat transfer area, thereby improving the heat dissipation capacity.
[0041] S300, the total flow rate flowing into the inlet is pre-allocated into flow rates flowing into n sub-channels respectively. The sub-channels correspond one-to-one with the main channel. The flow rate allocation ratio of each sub-channel is set according to the weight of the corresponding heating area and / or the cooling amount.
[0042] This step, based on the heat-generating region classification (first-class heat-generating region and second-class heat-generating region) determined in step S100, uses regulating valves to pre-allocate the total flow rate into the liquid cooling plate in a differentiated manner, thereby achieving precise allocation of cooling resources. The flow allocation ratio of each sub-channel is set according to the weight of the corresponding heat-generating region and / or the cooling amount, and remains unchanged in subsequent optimization processes.
[0043] Specifically, let the total flow rate into the liquid cooling plate inlet be Q. A main channel is set up after the inlet, and the main channel is connected to n sub-channels via multiple regulating valves. The end of each sub-channel is connected to the inlet of a passage. By presetting the opening degree of each regulating valve, the total flow rate Q is divided into n parts, which flow into the n sub-channels respectively.
[0044] According to the classification in step S100, the first type of heat-generating areas (GPU chip area and memory area) require greater heat dissipation capacity when the workload changes, while the second type of heat-generating areas (other heat-generating areas) have relatively stable heat dissipation requirements. Therefore, this embodiment sets the flow allocation ratio of each sub-channel to satisfy the following: the flow allocated to the path corresponding to the first type of heat-generating area is greater than the flow allocated to the path corresponding to the second type of heat-generating area. To simplify the structure and highlight the flow guarantee of the core area, the main channel can be divided into three sub-channels, corresponding to the chip area, memory area, and other heat-generating areas, respectively.
[0045] Specifically: The first data stream (denoted as Q1) is input to the path corresponding to the GPU chip region through the first sub-channel; The second flow (denoted as Q2) is input to the path corresponding to the video memory region through the second sub-channel; The third flow (denoted as Q3) is input to the pathway corresponding to other heat-generating areas through the third sub-channel.
[0046] In the above allocation method, the first flow rate is greater than the second flow rate, and the second flow rate is greater than or equal to the third flow rate, thereby realizing the tilting allocation of cooling resources to the core heat-generating area.
[0047] To quantitatively describe the relationship between the flow distribution ratio of each sub-channel and the weight of the heating zone and / or the cooling amount, let the weight of the j-th heating zone be w. j The cooling rate is ΔT j The flow rate Q allocated to the corresponding sub-channel of the heating area is then... j It can be represented as: Q j =Q·f(wj ΔT j ).
[0048] Where f() is the allocation function, and the sum of the allocation function values corresponding to all heating areas is equal to 1.
[0049] As a specific implementation of this embodiment, the allocation function adopts a normalized weighted product form: f(w j ΔT j ) = (w j ·ΔT j ) / S, where S is the total weighted cooling amount, which is the sum of the products of the weights of all heating areas and the cooling amount.
[0050] The weights can be pre-set based on the importance of the heat-generating areas; for example, the chip area has the highest weight, followed by the memory area, and other areas have the lowest. The cooling amount reflects the required heat dissipation intensity of the area; the greater the cooling amount, the more cooling resources the area needs. Through the above expressions, the flow allocation ratio of each sub-channel is positively correlated with the weight of the heat-generating area and the cooling amount, achieving precise allocation of cooling resources.
[0051] In a preferred implementation of this embodiment, based on engineering experience, the weights for the chip region are set as w1=0.8, the memory region as w2=0.1, and other regions as w3=……=wn=0.1 / n. Substituting these values into the above formula and considering the cooling amount of each region, the flow distribution ratio for each sub-channel can be calculated. When the cooling amounts for the chip region and the memory region are similar, this preferred method yields a distribution result of Q1=0.8×Q, Q2=0.1×Q, and Q3=0.1×Q. That is, 80% of the cooling flow is allocated to the chip region, and the memory region and other regions each receive 10% of the cooling flow.
[0052] Through the aforementioned pre-allocation of flow, a precise match between cooling resources and heat dissipation requirements is achieved. It should be noted that this flow allocation ratio is preset and fixed by adjusting the valve opening, and remains unchanged during the subsequent optimization process in step S500. When optimizing the horizontal side length of each passage in step S500, the inlet flow boundary condition for each passage is the pre-set flow value for this step.
[0053] S400, establish a three-dimensional computational fluid dynamics simulation model that includes the liquid cooling plate flow channel structure and the GPU structure.
[0054] This step establishes a three-dimensional computational fluid dynamics (CFD) simulation model for subsequent parameter optimization iterations, based on the liquid-cooled plate flow channel structure constructed in step S200 and the flow distribution scheme determined in step S300.
[0055] Specifically, the three-dimensional computational fluid dynamics simulation model includes a liquid cooling plate flow channel structure and a simplified GPU structure. The simplified GPU structure is modeled based on the heat-generating region division determined in step S100, including simplified geometric models of the chip region, memory region, and other heat-generating regions. Each heat-generating region is set as an independent heat source boundary condition in the model.
[0056] In this embodiment, the establishment of the three-dimensional computational fluid dynamics simulation model includes the following settings: (1) Geometric model Based on the liquid cooling plate flow channel structure parameters determined in step S200 (including the horizontal side length, vertical side length a, channel length L, and rotation path shape of each channel), a complete geometric model of the liquid cooling plate is established using 3D modeling software. Simultaneously, a simplified geometric model of the GPU is established according to its actual size and the distribution of each heat-generating area. To simplify calculations, the GPU chip area, memory area, and other heat-generating areas are simplified as planar heat sources or block heat sources, and the position coordinates of each heat-generating area on the GPU motherboard are precisely set. The contact surfaces of the liquid cooling plate and the GPU are matched and assembled to ensure accurate correspondence of the heat transfer interfaces.
[0057] (2) Grid division After completing the geometric modeling, the computational domain is discretized using either unstructured or structured meshes to ensure that the mesh quality meets the computational accuracy requirements. Local mesh refinement is performed at the fluid-structure interface to accurately capture the temperature and velocity gradients within the heat transfer boundary layer.
[0058] (3) Material parameter settings To accurately simulate the heat transfer and flow processes, the material thermophysical parameters of each structure involved in the model are set, including: Thermal conductivity, density, and specific heat capacity of liquid cooling plate materials; Thermal conductivity, density, and specific heat capacity of GPU motherboard materials; Thermal conductivity, density, specific heat capacity, and dynamic viscosity of the cooling liquid; Thermal conductivity, density, and specific heat capacity (if applicable) of the heat-conducting medium.
[0059] (4) Boundary condition settings Based on the flow allocation scheme determined in step S300, set the boundary conditions for the model: Inlet boundary conditions: Inlet flow boundary conditions are set for each passage at the inlet boundary corresponding to each independent inlet. Specifically, the flow rate of the first sub-channel is defined as Q1, the flow rate of the second sub-channel as Q2, the flow rate of the third sub-channel as Q3, and so on until the flow rate of the nth sub-channel is Q... n And set the inlet coolant temperature; Outlet boundary conditions: Set pressure boundary conditions at the outlet, usually set to a relative static pressure of 0 Pa; Heat transfer boundary conditions: Set the solid-solid heat transfer boundary parameters between the liquid cooling plate and the GPU, and the liquid-solid heat transfer boundary parameters between the inner wall of the liquid cooling plate and the cooling liquid; Heat source boundary conditions: Set the surface heat source temperature or heat flux density of multiple heat-generating areas on the GPU motherboard as the active heat source input for the model; Other boundary conditions: Set other external surfaces besides the above boundaries as adiabatic boundary conditions, and set the interface between the fluid domain and the solid domain as a no-slip wall condition.
[0060] (5) Physics field model and solution settings A conjugate heat transfer model is used to couple the flow and heat transfer in the fluid domain and the heat conduction in the solid domain. The fluid domain employs either a k-epsilon turbulence model or a laminar flow model (determined based on the Reynolds number), and the following governing equations are solved: The mass conservation equation (continuity equation): ▽·(ρu)=0.
[0061] Where ρ is the fluid puzzle, u is the fluid velocity vector, and ▽ is the Hamiltonian operator.
[0062] Momentum conservation equation (Navier-Stokes equation): ▽·(ρuu)=-▽p+▽·(μ(▽u+(▽u)) T ))+F.
[0063] Where p is pressure, μ is fluid dynamic viscosity, and F is volume force term (such as porous media resistance term or thermal buoyancy term).
[0064] Energy conservation equation: ▽·(ρc p uT)=▽·(k▽T)+S T .
[0065] Among them, c p Here, T is the specific heat capacity at constant pressure, k is the temperature, and S is the thermal conductivity. T This refers to heat source terms (such as viscous dissipation terms or external heat sources).
[0066] Set up a steady-state solution mode and define the convergence criterion as residuals less than 1 × 10⁻⁶. -5 And set the maximum number of iterations.
[0067] (6) Temperature monitoring point setup and regional temperature characterization To accurately evaluate the heat dissipation effect of each heat-generating region, multiple discrete temperature monitoring points are set within each region. In this embodiment, nine temperature monitoring points are set in each heat-generating region, evenly distributed on the geometric surface of that region. After the simulation is completed, the temperature values of each monitoring point are extracted, a monitoring point result output file is set, and the stable temperature values of the monitoring points in each region are output.
[0068] In this embodiment, the arithmetic mean of the temperature values of multiple monitoring points in each heating area is used as the temperature monitoring value of that heating area.
[0069] Using multi-point sampling averaging as a method to characterize regional temperature has the following technical significance: Traditional optimization methods typically use single-point temperature (such as the highest temperature or the temperature of a representative point) as the optimization target, which can easily lead to over-responding to local hot or cold spots during the optimization process, thereby distorting the flow channel structure and affecting the overall heat dissipation performance. This scheme uses multi-point average temperature as the optimization target, which can more accurately characterize the overall thermal state of the region, avoid structural design deviations caused by local temperature anomalies, and improve the engineering applicability and robustness of the optimization results.
[0070] After completing the above settings, the solution file of the simulation model is output for subsequent step S500 to perform parameter optimization and iterative calculations.
[0071] S500, taking the horizontal side length of each channel as the optimization variable, and taking the deviation of the simulated temperature monitoring value of each heating area from the preset temperature expectation value as the target, substitutes the optimization variable into the three-dimensional computational fluid dynamics simulation model, and uses a filtering optimization algorithm to iteratively optimize until the optimization result that satisfies the preset condition is obtained.
[0072] (1) Optimize the convergence conditions of the target domain The optimization goal of this step is to make the temperature monitoring values of each heating zone as close as possible to the preset expected temperature value. To quantify this goal and set convergence conditions, the relative deviation is defined as: δ j =|T j mT j c | / T j c .
[0073] The preset condition is: for each heating area, the relative deviation is less than 5%, i.e., δ j <5%.
[0074] The 5% threshold setting is based on engineering experience: when the temperature deviation is controlled within 5%, the heat dissipation system can meet the stable operation requirements of most GPU chips. At the same time, this threshold also provides a reasonable convergence criterion for the optimization algorithm, avoiding the waste of computing resources due to the pursuit of excessively high precision.
[0075] (2) Working principle of ensemble Kalman filter algorithm In this invention, the filtering optimization algorithm is the ensemble Kalman filter algorithm. The ensemble Kalman filter (EnKF) is a recursive filtering algorithm suitable for nonlinear systems. Its core idea is to use a set of state variables to estimate the probability distribution of the system, and then update the set using observation data to obtain the optimal state estimate.
[0076] In this optimization problem, the state variables to be optimized are the horizontal side lengths of n pathways, and the observed data are the temperature monitoring values of each heating region obtained through CFD simulation. The algorithm achieves parameter optimization through the following mechanism: Prediction steps: Based on the current set of state variables, predict the corresponding temperature monitoring values through a CFD simulation model to form a state-observation pair; Update steps: Calculate the Kalman gain based on the deviation between the predicted temperature and the target temperature (preset expected temperature value), and perform a weighted update on the set of state variables so that the updated state variables are more likely to produce observations close to the target temperature. Iterative loop: The updated set of state variables is used as the initial value for the next iteration. The prediction and update steps are repeated until the state variables converge or the preset conditions are met.
[0077] This algorithm can effectively handle the highly nonlinear and parameter coupling problems of CFD simulation models, avoid getting trapped in local optima, and make full use of historical simulation data to improve optimization efficiency.
[0078] (3) Algorithm implementation steps in this embodiment To achieve the above optimization process, this embodiment adopts the following specific steps: S510, Create a set of prior parameters.
[0079] Based on the cooling amount of each heating zone determined in step S100, the horizontal side length b of each passage is allocated proportionally. j The greater the cooling rate, the larger the heat exchange area required in that region; therefore, the horizontal side length of the corresponding passage should be larger. The principle of proportional allocation is: b j ∝ΔT j That is, the initial side length of each passage is proportional to the cooling amount of the corresponding heating area.
[0080] Based on the above principles, the first set of variable samples is formed: z1 = (b1) 1 b1 2 ...,b1 j ...,b1 nb1 j Let be the initial horizontal side length of the j-th pathway in the first set of variable samples.
[0081] S520, based on the first set of variable samples, multiple sets of variable samples are generated by adjusting the horizontal side lengths of different paths to form an initial set of variables.
[0082] Based on the first set of variable samples, multiple sets of variable samples are generated through a step size adjustment strategy to form an initial set of variables with sufficient diversity to cover the possible optimization space.
[0083] Let the step size be Δb (Δb is a small positive number, the size of which is determined according to the range of values of the design variables and the accuracy requirements), the generation method is as follows: Increase the horizontal side length of the (r-1)th path by a step Δb, and decrease the horizontal side length of the rth path by a step Δb to generate a new set of variable samples, where r takes the value from 2 to n. Increase the horizontal side length of the nth path by a step size Δb, and decrease the horizontal side length of the 1st path by a step size Δb to generate another set of variable samples.
[0084] Following the above pattern, starting from the second group, a total of n new variable samples are formed: z2, z3, ..., z n+1 .in, z2 = (b1) 1 +△b,b1 2 -△b,……,b1 3 ...,b1 n ); z3 = (b1) 1 b1 2 +△b,……,b1 3 -△b,……,b1 n ); z n =(b1 1 b1 2 ...,b1 n-1 -△b,b1 n +△b); z n+1 =(b1 1 -△b,b1 2 ...,b1 n-1 b1 n +△b).
[0085] The first set of variable samples z1 and the newly generated n sets of variable samples together constitute the initial set of variables E={z1, z2, z3, ..., z n+1 There are a total of n+1 sets of variable samples.
[0086] S530, Substitute each set of variable samples in the initial set of variables into the three-dimensional computational fluid dynamics simulation model for solution, and obtain the corresponding temperature monitoring value matrix of each heating region.
[0087] Substitute each set of variable samples from the initial variable set E into the three-dimensional computational fluid dynamics simulation model established in step S400 for solution. For each set of samples, extract the temperature monitoring values of each heating region to form a temperature state parameter matrix P.
[0088] Specifically, for the k-th sample group (k=1,2,...,n+1) in E, the temperature monitoring value T of each heating region is obtained through CFD simulation. k1 m, T k2 m, ..., T kj m, ..., T kn m, then the temperature state vector corresponding to the kth sample group is: P k =(T k1 m, T k2 m, ..., T kj m, ..., T kn m).
[0089] The temperature state vectors of all samples together constitute the temperature state parameter matrix P.
[0090] S540, based on the deviation between the temperature monitoring value of each heating area and the preset temperature expectation value, select the set of variable samples with the smallest deviation from the initial set of variables as the initial value for the next iteration.
[0091] After obtaining the temperature state parameter matrix P, based on the deviation between the monitored temperature values of each heating region and the preset expected temperature values, the set of variable samples with the smallest deviation is selected from the initial set of variables as the initial values for the next iteration. The specific process is as follows: First, calculate the average relative deviation for each group of samples. The average relative deviation of the k-th group of samples is equal to the sum of the relative deviations of all heat-generating areas divided by the number of heat-generating areas n, where the relative deviation of each heat-generating area is the difference between the temperature monitoring value of that area and the preset expected temperature value divided by the preset expected temperature value.
[0092] Next, the samples are sorted in ascending order of average relative deviation. The smaller the average relative deviation, the closer the simulation result of that group of samples is to the target temperature, and the better its structural parameters.
[0093] Finally, the set of variable samples with the smallest average relative deviation after sorting is selected as the initial value for the next iteration.
[0094] This selection strategy has the following technical significance: due to the high nonlinearity and computational cost of CFD simulation models, generating an initial set through prior knowledge and selecting the optimal one as the starting point for iteration after simulation evaluation can significantly reduce the number of subsequent iterations and improve optimization efficiency.
[0095] (4) Iteration loop and convergence judgment Using the optimal variable sample selected in S540 as the new initial state, repeat steps S520 to S540 for iterative optimization. After updating the horizontal side length of the pathway in each iteration, perform the following dynamic coupling control: (1) Based on the flow-size coupling relationship model, the flow distribution ratio of the corresponding sub-channel is synchronously corrected to form a closed-loop control of flow channel size optimization and flow distribution correction.
[0096] In this invention, the flow-size coupling model is: λ j =g·(Q j / b j ) 1 / 2 .
[0097] Where, λ j Let g be the flow-size coupling coefficient of the j-th sub-channel, and g be an empirical coefficient. The empirical coefficient g is determined based on GPU liquid cooler heat dissipation test calibration, and its value ranges from 0.8 to 1.2.
[0098] This coupling model reflects the degree of matching between flow rate and channel size: when the flow rate is large and the horizontal side length is small, the flow rate-size coupling coefficient increases, indicating that the flow resistance may be too large, and the side length needs to be increased or the flow rate needs to be reduced; when the flow rate is small and the horizontal side length is large, the flow rate-size coupling coefficient decreases, indicating that the heat dissipation area may be wasted, and the side length needs to be reduced or the flow rate needs to be increased.
[0099] After updating the horizontal side length in each iteration, the coupling coefficient under the current traffic allocation ratio is calculated according to the above coupling relationship model, and the traffic allocation ratio of the corresponding sub-channel is corrected accordingly to make the coupling coefficient value approach the optimal coupling range.
[0100] (2) If the deviation between the corrected flow allocation ratio and the initial pre-allocation ratio exceeds the preset ratio deviation, for example, 10%, then the flow pre-allocation in step S300 is re-executed to achieve closed-loop control of “flow channel size optimization - flow allocation correction”.
[0101] Through the above dynamic coupling control, the flow rate and channel size of each channel are always reasonably matched, avoiding excessive flow resistance or waste of heat dissipation area due to changes in channel size, thereby achieving a balance between heat dissipation efficiency and flow resistance.
[0102] Subsequently, the corrected flow allocation ratio is used as a new boundary condition and substituted into the next iteration of CFD simulation solution.
[0103] After each iteration, check whether the preset condition δ is met. j <5% holds true for all j=1……n. If this condition is met, the iteration terminates, and the current variable sample is output as the optimization result; if not, the iteration continues until the maximum number of iterations is reached or convergence occurs.
[0104] (5) Parallel computing and intelligent scheduling Since each iteration requires n+1 CFD simulation calculations (corresponding to n+1 sets of variable samples in the initial variable set), the computational load is large, and direct serial execution would lead to an excessively long optimization cycle. To improve optimization efficiency, this embodiment adopts the following parallel computing strategy: During each iteration, the solution files for n+1 sets of 3D computational fluid dynamics simulation models corresponding to the initial set of current variables are output. A supercomputer system computation task submission script is written to submit each set of solution files to the supercomputer system. The supercomputer system is equipped with a job scheduling system (such as SLURM or PBS). By writing corresponding job submission scripts, multiple sets of simulation tasks can be submitted and executed in parallel. Each set of tasks is solved synchronously on independent computing nodes without interference.
[0105] To further optimize computing resource allocation and avoid wasting computing resources due to average effort, this embodiment embeds temperature deviation-driven priority assignment logic into the job submission script. Specifically, based on the average relative deviation δ of each group of samples obtained from previous iterations... k Assign differentiated computing power priorities to the n+1 groups of CFD simulation tasks: Scheduling Priority: The larger the average relative deviation, the more severe the temperature deviation of the sample group from the target, and the more priority its structural parameters need to be optimized. Therefore, a higher scheduling priority should be assigned to this type of task. For example, in the SLURM job scheduling system, this can be achieved by setting a priority parameter, assigned as priority=100-δ. k ×100, where δ k Substituting percentage values, the larger the deviation, the higher the priority value, and the job scheduling system prioritizes allocating computing resources to high-priority tasks.
[0106] Computational resource allocation: For high-priority tasks, allocate more CPU cores and GPU memory to accelerate the solution process; for low-priority tasks, use the basic computing power configuration. For example, the number of CPU cores allocated to the k-th group of tasks... k It can be set to: cores k =cores kbase ×(1+δ k ), where cores k base This is based on the number of cores. Through the above strategy, computing power is directed towards samples that urgently need optimization, reducing ineffective computing power consumption and improving overall computing efficiency.
[0107] During the CFD simulation process, real-time monitoring and termination logic is embedded to avoid converging tasks from consuming computing resources. For each set of parallel simulation tasks, the temperature convergence residual of the iteration step is calculated in real time. The residual is defined as the temperature value of the current iteration step minus the temperature value of the previous iteration step.
[0108] The early termination command for this group of tasks will be automatically triggered when the following conditions are met: Condition 1: The absolute value of the residuals for five consecutive iterations is less than a preset convergence residual threshold. In this embodiment, the preset convergence residual threshold can be 10. -3 ℃; Condition 2: The average relative deviation between the current temperature state vector and the target value is less than 50% of the optimal deviation value achieved by this group of samples in the previous iteration.
[0109] When both of the above conditions are met, an early termination command is automatically triggered (e.g., terminating the task via the scancel command in the SLURM job scheduling system), and the currently converged solution results are saved. Tasks that do not meet the termination conditions continue execution until the preset number of iterations.
[0110] This early termination mechanism effectively prevents converged tasks from continuing to occupy computing power, dynamically allocating computing resources to tasks that have not yet converged or are converging slowly, thereby further improving overall iteration efficiency.
[0111] After the simulation is completed, the temperature simulation results for each heating region are extracted from each solution result file to obtain the temperature state parameter matrix P. Based on this matrix, set rearrangement and initial value selection for iteration are performed to proceed to the next iteration.
[0112] Through the parallel computing strategy described above, the time for a single iteration is reduced from (n+1) times the time for a single simulation when executed serially to approximately equal to the time for a single simulation, which significantly improves the optimization efficiency and makes iterative optimization based on CFD simulation feasible in engineering practice.
[0113] Repeat the above iterative calculation steps until the preset conditions are met, and finally obtain the required combination of liquid cooling plate structural parameters.
[0114] (6) Preferred Implementation Example 1: Deviation Calculation Introducing Temperature Response Weighting Coefficient As a preferred embodiment of the present invention, in the average relative deviation calculation of S540 above, a temperature response weighting coefficient can be further introduced to reflect the priority differences of different heat-generating regions in heat dissipation optimization. The corrected average relative deviation δ of the k-th sample group... k The calculation formula is as follows: First, for each heat-generating area, calculate the difference between the monitored temperature value and the preset expected temperature value, and then divide it by the preset expected temperature value to obtain the relative deviation of that area; then, multiply the relative deviation of the heat-generating area by the temperature response weight of that area to obtain the weighted relative deviation of that heat-generating area; next, sum the weighted relative deviations of all heat-generating areas to obtain the summation result; finally, divide the summation result by the total number of heat-generating areas n to obtain the corrected average relative deviation δ of the k-th sample group. k Based on the temperature response characteristics of different heat-generating areas of the GPU, the chip area has the fastest temperature response and the highest requirement for immediate heat dissipation, followed by the memory area, with other areas having the slowest temperature response. Based on these characteristics, this embodiment sets the following values: 0.6 for the chip area, 0.3 for the memory area, and 0.1 for other areas.
[0115] The variable samples are sorted in descending order of the corrected average relative deviation, and the set of variable samples with the smallest deviation is selected as the initial value for the next iteration. By introducing a temperature response weighting coefficient, the deviation calculation is made more consistent with the heat dissipation priority of each heat-generating area of the GPU, improving the rationality of the initial value for iteration and accelerating the convergence speed.
[0116] (7) Preferred Implementation Example 2: Parallel Strategy for Sample Hierarchy In another preferred embodiment of the present invention, during the CFD simulation solution process of S530 above, the variable samples are divided into two priority levels: High-priority samples: δ k ≥0.05, meaning the average relative deviation is greater than or equal to 5%, indicates that the temperature of this sample group deviates significantly from the target and needs to be optimized first. Low priority samples: δ k <0.05, meaning the average relative deviation is less than 5%, indicates that the sample group is close to the target temperature and the urgency for optimization is low.
[0117] For samples of different priorities, allocate supercomputing nodes with different performance levels and simulation iteration step sizes: High-priority samples: Allocate supercomputing high-performance computing nodes (e.g., CPU cores ≥ 64, video memory ≥ 128GB) and set shorter simulation iteration steps (e.g., 50 steps / time) to quickly obtain convergence results; Low-priority samples: Allocate regular computing nodes (e.g., CPU cores = 32, video memory = 64GB) and set a regular simulation iteration step size (e.g., 100 steps / time) to save computing resources while ensuring computational accuracy.
[0118] By employing the aforementioned sample-level parallel strategy, differentiated allocation of computing resources can be achieved, reducing ineffective computing power consumption and further improving iteration efficiency.
[0119] The method provided by this invention has at least the following technical effects: (1) Realize customized liquid cooling plate design for specific application scenarios This invention divides the liquid cooling plate flow channel into multiple independent parallel paths corresponding to each heat-generating area. By combining the cooling amount of each heat-generating area with a preset temperature expectation, the total flow rate is pre-allocated differentially, ensuring precise matching of cooling resource configuration with the heat dissipation needs of each area. Based on this, using the horizontal side length of each path as the optimization variable and meeting preset temperature deviation conditions as the objective, a filtering-based optimization algorithm is employed for parameter optimization. This allows for the efficient customization and development of liquid cooling plate structures that meet diverse heat dissipation requirements for specific GPU work scenarios in supercomputing centers or enterprises (such as graphics rendering, AI computing, and scientific data analysis), overcoming the limitations of traditional uniform flow channel designs that cannot adapt to diverse scenarios.
[0120] (2) Achieve precise allocation of cooling resources and energy conservation Compared to traditional global channel distribution designs or hotspot area channel encryption designs, this invention, based on the hotspot distribution and temperature rise characteristics of the GPU under low and full load conditions, uses independent sub-channel design and ensemble Kalman filtering optimization methods to collaboratively optimize the flow distribution ratio and channel cross-sectional dimensions of each path. Furthermore, by introducing a flow-size coupling control mechanism, the matching relationship between flow distribution and channel dimensions is simultaneously corrected during iterative optimization, ensuring a reasonable match between flow rate and cross-sectional dimensions in each path, and avoiding excessive flow resistance or wasted heat dissipation area due to changes in channel dimensions. This solution can achieve a balance between heat dissipation efficiency and flow resistance while ensuring effective heat dissipation and avoiding ineffective consumption of coolant, electricity, and other energy sources.
[0121] (3) Shorten the R&D cycle and improve industrialization efficiency This invention leverages the parallel computing capabilities of supercomputers and virtual simulation technology. Through a sample-level parallel strategy, temperature-biased priority scheduling, and an early termination mechanism, it significantly improves the computational efficiency of multiple CFD simulation tasks in each iteration. This reduces the single iteration time from (n+1) times the single simulation time in serial execution to approximately equal to the single simulation time. This technical solution enables rapid optimization of the structural parameters and performance verification of supporting liquid cooling plates during the development or initial market launch phase of new GPU products. It allows for the parallel advancement of liquid cooling plate design and GPU product development, effectively reducing design iteration costs and providing technical support for liquid cooling plate manufacturers to quickly respond to market demands.
[0122] This invention also provides an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being configured to perform the method described in this invention.
[0123] This invention also provides a computer-readable storage medium storing computer-executable instructions for performing the methods described in this invention.
[0124] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.
[0125] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.
Claims
1. A simulation optimization design method for a GPU liquid cooling plate, characterized in that, The method includes the following steps: S100, determine n heat-generating areas of the GPU and the preset temperature expectation value and cooling amount of each heat-generating area, wherein the cooling amount is determined based on the difference between the operating temperature of the heat-generating area and the preset temperature expectation value. S200, construct a liquid cooling plate flow channel structure, the liquid cooling plate flow channel structure includes an inlet, an outlet and n parallel channels connecting the inlet and the outlet, each channel has a different horizontal side length and corresponds to a heating area. S300, the total flow rate into the inlet is pre-allocated into the flow rates into n sub-channels respectively. The sub-channels correspond one-to-one with the main channel. The flow rate allocation ratio of each sub-channel is set according to the weight of the corresponding heating area and / or the cooling amount. S400, establish a three-dimensional computational fluid dynamics simulation model that includes the liquid cooling plate flow channel structure and the GPU structure; S500, taking the horizontal side length of each channel as the optimization variable, and taking the deviation of the simulated temperature monitoring value of each heating area from the preset temperature expectation value as the target, substitutes the optimization variable into the three-dimensional computational fluid dynamics simulation model, and uses a filtering optimization algorithm to iteratively optimize until the optimization result that satisfies the preset condition is obtained.
2. The method according to claim 1, characterized in that, The n heat-generating areas include a first type of heat-generating area and a second type of heat-generating area. The first type of heat-generating area needs to dynamically adjust its heat dissipation capacity when the workload changes, while the second type of heat-generating area maintains a stable heat dissipation requirement when the workload changes. In S300, the flow rate allocated to the path corresponding to the first type of heat-generating area is greater than the flow rate allocated to the path corresponding to the second type of heat-generating area.
3. The method according to claim 2, characterized in that, The first type of heat-generating area includes at least the GPU chip area and the video memory area.
4. The method according to claim 1, characterized in that, In S500, the filtering optimization algorithm is the ensemble Kalman filter algorithm.
5. The method according to claim 4, characterized in that, The parameter optimization using the ensemble Kalman filter algorithm includes: S510: Based on the cooling amount of each heat-generating area, the horizontal side length of each passage is proportionally allocated to form the first set of variable samples; S520, Based on the first set of variable samples, multiple sets of variable samples are generated by adjusting the horizontal side lengths of different paths to form an initial set of variables; S530, Substitute each set of variable samples in the initial set of variables into the three-dimensional computational fluid dynamics simulation model for solving, and obtain the corresponding temperature monitoring value matrix of each heating region; S540, based on the deviation between the temperature monitoring value of each heating area and the preset temperature expectation value, select the set of variable samples with the smallest deviation from the initial set of variables as the initial value for the next iteration.
6. The method according to claim 5, characterized in that, In S520, the method for generating multiple sets of variable samples includes: Increase the horizontal side length of the (r-1)th path by one step, and simultaneously decrease the horizontal side length of the rth path by the same step to generate a new set of variable samples, where r takes values from 2 to n; and, Increase the horizontal side length of the nth path by the step size, while decreasing the horizontal side length of the 1st path by the step size to generate another set of variable samples.
7. The method according to claim 1, characterized in that, In S400, the establishment of the three-dimensional computational fluid dynamics simulation model includes: Set the material parameters for the liquid cooling plate, GPU motherboard, cooling liquid, and heat transfer medium; Set the inlet flow boundary conditions for n channels and the total outlet pressure boundary conditions. Set the liquid-solid heat transfer boundary parameters and the solid-solid heat transfer boundary parameters; The k-epsilon turbulence model was adopted; Multiple temperature monitoring points are set up in each heat-generating area, and the average temperature value of the multiple temperature monitoring points is taken as the temperature monitoring value of the heat-generating area.
8. The method according to claim 1, characterized in that, The method further includes: in each iteration, outputting the solution file of the three-dimensional computational fluid dynamics simulation model, writing a supercomputer system computation task submission script, and using the supercomputer for parallel computation to obtain the solution results.
9. An electronic device, characterized in that, Including processor and memory; The processor executes the steps of the method as described in any one of claims 1 to 8 by invoking programs or instructions stored in the memory.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a program or instructions that cause a computer to perform the steps of the method as described in any one of claims 1 to 8.