Fluid field visualization interaction method, system, device with force feedback and storage medium

Abstract

The present application relates to the technical field of fluid mechanics intelligent simulation, in particular to a fluid field visualization interaction method, system and device with force feedback and a storage medium, the method comprising: obtaining fluid physical parameters of a target fluid scene; converting the fluid physical parameters into fluid lattice unit parameters; calculating a Reynolds number based on the fluid physical parameters and the fluid lattice unit parameters; performing fluid simulation calculation according to the fluid lattice unit parameters and rendering a fluid image according to the fluid simulation calculation result; calculating a gain haptic force of the fluid based on the Reynolds number and the fluid simulation calculation result; and sending the gain haptic force to an interaction unit, which is configured to output force haptic feedback of the fluid according to the gain haptic force. The present application has the beneficial effects of convenient use and precise fluid force feedback.

Description

Technical Field

[0001] This invention relates to the field of intelligent simulation technology in fluid mechanics, specifically to a method, system, device, and storage medium for visualizing and interacting with fluid fields using force feedback. Background Technology

[0002] Fluid mechanics is a fundamental discipline in engineering and physics, but its core concepts (such as Reynolds number, von Kármán vortex street, drag and lift) are highly abstract. In teaching fluid mechanics, it is difficult to establish an intuitive connection between the kinematic description of fluids (how fluids move) and the dynamic explanation (why fluids move in this way). Traditional teaching methods mainly rely on lectures and mathematical derivations, which fail to help students bridge the gap between abstract mathematical forms and concrete physical phenomena. In recent years, with the continuous development of scientific visualization and multimodal interactive technologies, technical solutions for fluid mechanics simulation have emerged, enabling an intuitive display of the motion state of fluids and providing new possibilities for solving this problem. However, existing fluid simulation technologies mainly suffer from the following technical problems: Existing fluid dynamics teaching systems lack tactile feedback: Traditional computational fluid dynamics (CFD) simulations based on the Navier-Stokes equations and GPU-accelerated real-time fluid simulations mainly rely on visual presentation of flow field information, lacking other sensory channels such as touch. The forces exerted by fluids on objects (drag, lift) are important physical quantities, but existing systems can only indirectly display them through numerical displays or graphs, preventing learners from directly "feeling" the existence and changing characteristics of these forces.

[0003] Existing haptic rendering technologies are not specifically designed for fluid mechanics teaching, lacking instructional modules and parameter simplification mechanisms. While SPH (Smooth Particle Hydrodynamics) haptic rendering technology integrates fluid and tactile sensations, its application is geared towards entertainment applications such as virtual cooking, rather than fluid mechanics education. Furthermore, its force feedback gain method is simplistic and fails to reflect the differences in flow patterns driven by Reynolds number. Existing haptic rendering technologies typically use a fixed gain coefficient to linearly amplify the simulated force before direct output, completely decoupling the gain process from the physical state of the flow. Regardless of whether the flow field is in laminar or turbulent regions, haptic feedback only reflects differences in force amplitude, with time-frequency characteristics remaining unchanged. Users cannot perceive the essential turbulent characteristics such as increased pulsation and multi-scale vortex structures that appear with increasing Reynolds number through touch, thus weakening the effectiveness of embodied cognition in fluid mechanics teaching.

[0004] There is a conflict between computational methods and the need for real-time interaction. Traditional CFD simulation methods (finite volume method, finite element method) offer high computational accuracy but are time-consuming, making real-time interaction difficult. While GPU real-time fluid technology is fast, it is usually visually oriented and struggles to provide accurate force calculations. Haptic rendering has strict requirements on computational frequency (typically 1000Hz), posing a challenge to the computational efficiency of fluid simulation.

[0005] The complex parameter inputs and high professional threshold mean that while lattice unit parameters in fluid mechanics (such as relaxation time, lattice velocity, and lattice viscosity) are fundamental knowledge for fluid mechanics professionals, they are difficult for ordinary learners (such as high school students, non-STEM university students, and science enthusiasts) to understand their physical meaning or judge reasonable value ranges based on everyday experience. The lack of physical unit mapping prevents learners from corresponding simulation results with real-world physical scenarios, diminishing the practical significance of learning. Summary of the Invention

[0006] The purpose of this invention is to provide a method, system, device, and storage medium for visualizing and interacting with fluid fields with force feedback, in order to solve the technical problems of the existing technology, such as the single fluid force feedback gain method, complex parameter input, and high professional threshold.

[0007] In a first aspect, the present invention provides a method for visualizing and interacting with fluid fields with force feedback, comprising the following steps: Obtain the fluid physical parameters of the target fluid scene, convert the fluid physical parameters into fluid lattice unit parameters, and calculate the Reynolds number based on the fluid physical parameters and fluid lattice unit parameters; Fluid simulation calculations are performed based on the parameters of the fluid lattice unit, and fluid images are rendered based on the simulation results. The gain tactile force of the fluid is calculated based on the Reynolds number and fluid simulation results; Amplified tactile force is sent to an interactive unit, which outputs force tactile feedback of the fluid based on the amplified tactile force.

[0008] The significant advantages of this invention are: by converting fluid physical parameters into fluid lattice unit parameters, users only need to input conventional fluid physical parameters in actual use, making it convenient for non-professionals. At the same time, it can realize the mapping between fluid simulation and physical units, making it easy for learners to correspond simulation results with real physical scenarios, which can greatly improve the learning effect of fluid mechanics.

[0009] Furthermore, this scheme calculates the amplified tactile force through the Reynolds number, and determines the relative dominance of fluid inertial and viscous forces based on the Reynolds number. This allows the amplified tactile force to directly correspond to the phase transition between laminar and turbulent flow. Moreover, by adjusting the Reynolds number, it can achieve both low-to-medium frequency large-scale oscillations corresponding to KAMAN vortex street shedding and high-frequency small-scale jitters corresponding to boundary layer separation in the fluid field. This ensures that users can perceive the essential characteristics of turbulence, such as increased pulsation and multi-scale vortex structures, as the Reynolds number increases, through tactile feedback, thus improving the effectiveness of embodied cognition in fluid mechanics teaching.

[0010] Furthermore, the calculation of the fluid gain tactile force based on the Reynolds number and fluid simulation results includes: Calculate the Reynolds number mixing factor based on the Reynolds number; Calculate high-frequency noise and low-frequency noise based on the Reynolds number mixing factor; Obtain the global gain coefficient, and calculate the gain lift and gain drag of the fluid based on the global gain coefficient, high-frequency noise, and low-frequency noise; Gain tactile force is calculated based on gain lift and gain drag.

[0011] By calculating the Reynolds number mixing factor, it is possible to achieve a transition from laminar to turbulent flow through Reynolds number control of the fluid field tactile feedback. This allows the output force feedback to conform to the smooth characteristics of laminar flow, while also reflecting the violent pulsations of fully developed turbulent flow, and simultaneously achieving a continuous transition from laminar to turbulent flow.

[0012] Furthermore, the calculation of high-frequency noise and low-frequency noise based on the Reynolds number mixing factor includes: Calculate the frequencies of high-frequency noise and low-frequency noise based on the Reynolds number mixing factor; Calculate the phase of high-frequency noise based on the frequency of high-frequency noise, and calculate the phase of low-frequency noise based on the frequency of low-frequency noise; High-frequency noise is generated based on the phase of high-frequency noise, and low-frequency noise is generated based on the phase of low-frequency noise.

[0013] Since high-frequency microscale tremors and low-frequency large-scale surges have different frequency evolution patterns, this scheme maintains independent phase variables for each to achieve smooth changes in noise frequency and avoid signal abrupt changes. Furthermore, this scheme calculates high-frequency microscale noise and low-frequency large-scale noise separately to ensure the statistical independence of microscale tremors and macroscale surges in the time domain and avoid artificial periodic overlap.

[0014] Furthermore, the formula for calculating the gain lift of the fluid is: In the formula, To increase lift, The global gain coefficient for lift. The original lift force of the fluid obtained from the simulation, The Reynolds number mixing factor, It is high-frequency noise. This is the high-frequency noise intensity coefficient. It is low-frequency noise. This refers to the low-frequency noise intensity coefficient. The formula for calculating the gain resistance of the fluid is: In the formula, Gain resistance, The global gain coefficient for resistance. The original fluid resistance is obtained from the simulation.

[0015] Furthermore, the migration strategy for fluid simulation calculation based on fluid lattice unit parameters is a pull-copy back-to-source mode. In the pull phase of the pull-copy back-to-source mode, the distribution function of the fluid simulation calculation is obtained and written into a temporary buffer. In the copy back-to-source phase of the pull-copy back-to-source mode, the data in the temporary buffer is copied back to the main buffer.

[0016] This scheme breaks down the migration strategy into two stages: pulling to a temporary buffer and writing back to the main buffer. Implicit synchronization acts as a barrier, ensuring data consistency and facilitating force computation. Simultaneously, it avoids the serialization overhead of atomic operations, fundamentally preventing write conflicts without the need for atomic operations.

[0017] Secondly, the present invention provides a fluid field visualization and interaction system with force feedback, applicable to the above-mentioned fluid field visualization and interaction method, including a fluid calculation unit and an interaction unit; The fluid computing unit is used to perform the steps described in the above-described fluid field visualization and interaction method; The interaction unit is used to provide human-computer interaction based on the execution results of the fluid computing unit.

[0018] Furthermore, the interactive unit includes a fluid visualization module and a tactile perception module. The fluid visualization module is used to provide fluid visual interaction, and the tactile perception module is used to provide force tactile feedback interaction based on the fluid rendering results.

[0019] By setting up visualization and tactile sensing modules to enable interaction, during fluid simulation, it is possible not only to clearly and intuitively observe the motion and trajectory of the fluid field based on images, but also to intuitively feel the force feedback of the flow field in the laminar or turbulent region through force tactile feedback, thereby improving the simulation effect of fluid.

[0020] Furthermore, the fluid computing unit is used to switch computing modes according to the motion state of the tactile sensing module, the computing modes including: In the high-precision tactile mode, when the position change rate of the tactile sensing module is greater than the position change rate threshold, the fluid computing unit performs force feedback updates at the first update frequency. In the energy-saving vision mode, when the tactile sensing module remains stationary for a period of time longer than the stationary time threshold, the fluid computing unit updates the force feedback at a second update frequency.

[0021] By switching different computing modes according to the different usage states of the tactile perception module, the frequency of simulation computing unit calls is reduced by 90% when the user is only visually observing, which reduces the CPU scheduling burden, frees up computing resources for visualization rendering, and avoids the loss of tactile interaction experience.

[0022] Thirdly, the present invention provides a fluid field visualization interaction device with force feedback, including a memory, a processor, a computer program stored in the memory, and an interaction device. The processor executes the computer program to implement the steps of the above-described fluid field visualization interaction method with force feedback, and the interaction device is used to provide fluid field visualization interaction with force feedback based on the processor execution result.

[0023] Fourthly, the present invention provides a computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, and when the computer program is executed by one or more processors, it implements the above-described method for visualizing and interacting with a fluid field with force feedback. Attached Figure Description

[0024] Figure 1 This is a flowchart of a fluid field visualization and interaction method with force feedback in an embodiment of the present invention. Figure 2 This is a schematic diagram of the pull-copy back-to-origin migration mode in an embodiment of the present invention; Figure 3 This is a schematic diagram of the fluid density field coloring mode in an embodiment of the present invention; Figure 4 This is a schematic diagram of the fluid velocity field coloring mode in the x-direction of an embodiment of the present invention; Figure 5 This is a schematic diagram of the coloring mode of the fluid velocity field in the y-direction in an embodiment of the present invention; Figure 6 This is a schematic diagram of the fluid velocity field coloring mode in an embodiment of the present invention; Figure 7 This is a schematic diagram of the fluid vortex field coloring mode in an embodiment of the present invention; Figure 8 This is a flowchart of a fluid field visualization and interactive system with force feedback in an embodiment of the present invention; Figure 9 This is a schematic diagram of the fluid visualization module interface in an embodiment of the present invention; Figure 10 This is a flowchart illustrating the adaptive time step adjustment process in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, a clear and complete description will be provided below in conjunction with the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0026] See appendix Figure 1 The illustrated interactive visualization method for fluid fields with force feedback includes the following steps: S1. Obtain the fluid physical parameters of the target fluid scene, convert each fluid physical parameter into a fluid lattice unit parameter, and calculate the Reynolds number based on the fluid physical parameters and the fluid lattice unit parameter; where the target fluid scene is the fluid scene to be simulated, and the fluid physical parameters include the fluid density, viscosity, velocity and geometric dimensions, where each fluid physical parameter can be obtained by measurement or calculation. When acquiring the fluid physical parameters of the target fluid scene, they can be transmitted to a computer platform with fluid simulation software installed via keyboard, storage medium or network.

[0027] When converting various fluid physical parameters into computational lattice unit parameters, this includes kinematic viscosity conversion and velocity conversion. The formula for kinematic viscosity conversion is as follows: In the formula, For lattice kinematic viscosity, For dynamic viscosity, For fluid density, For time step, The square of the spatial step size; The formula for calculating speed conversion is: In the formula, The inlet velocity is expressed in grid units. For the inlet velocity; In step S1, a stability check is also performed on the converted lattice unit parameters. Specifically, when checking the stability of the kinematic viscosity, the kinematic viscosity is verified based on the relaxation time to ensure the stability of the kinematic viscosity parameters. The relaxation time is calculated as follows: In the formula, Relaxation time; When judging the stability of kinematic viscosity based on relaxation time, if the relaxation time is within the relaxation range, the kinematic viscosity parameter is stable; otherwise, the kinematic viscosity parameter is not stable. Specifically, in this embodiment, the relaxation range is (0.5, 2.0), that is, when the relaxation time is greater than 0.5 and less than 2.0, the kinematic viscosity parameter is stable.

[0028] When performing a stability check on the converted velocity, the incompressibility assumption is guaranteed to be valid through a Mach number check, where the Mach number is calculated as follows: In the formula, Mach number, For the speed of sound, where ; When judging the stability of velocity based on Mach number, if the Mach number is less than the Mach threshold in the relaxation interval, the velocity parameter is stable; otherwise, the velocity parameter is not stable. Specifically, in this embodiment, the Mach threshold is 0.3, that is, when the Mach number is less than 0.3, the velocity parameter is stable.

[0029] If the stability check of kinematic viscosity or velocity fails, the physical parameters are adjusted, and the grid unit parameters are converted and checked again.

[0030] The Reynolds number is matched based on fluid physical parameters and fluid lattice unit parameters to ensure physical similarity of the Reynolds number. The formula for Reynolds number matching is as follows: In the formula, Let Reynolds number be 1. For the inlet speed, For characteristic geometric parameters, Kinematic viscosity, These are the characteristic geometric parameters within the lattice unit.

[0031] S2. Perform fluid simulation calculations based on the fluid lattice unit parameters. During the fluid simulation calculations, the fluid lattice unit parameter input values ​​are used on a computer platform equipped with the Unity engine. Real-time fluid simulation calculations are then performed on the GPU using the Lattice Boltzmann Method (LBM). Specifically, the FixedUpdate() function in the Unity engine executes Lattice Boltzmann method calculations and force outputs at a frequency of 1000Hz, implementing a high-frequency force feedback update mechanism. The Lattice Boltzmann Method is based on a mesoscopic-scale particle collision-transfer model, characterized by its simple algorithm, ease of parallelization, and ability to naturally handle complex boundary conditions. Specifically, during the fluid simulation calculations, the calculation process of the Lattice Boltzmann Method is decomposed into multiple independent computer core management programs, including boundary condition setting (SetBoundaries), collision steps (Collide), transfer steps (Stream_Pull, Stream_CopyBack), obstacle bounce (BarrierBounce), force calculation (ComputeBarrierForce), and curl calculation (ComputeCurl). Each core management program is independently scheduled and executed, with the correct computational order ensured through the GPU's hardware synchronization mechanism. Specifically, fluid simulation calculations include: The D2Q9 discrete velocity model is adopted, defining 9 discrete velocity directions. The D2Q9 discrete velocity model is as follows: In the formula, For the first Velocity vectors in each direction; The weighting coefficients for each discrete velocity direction are: In the formula, For the first Weighting coefficients for velocity vectors in each direction.

[0032] The single relaxation time model (BGK) collision is performed, and the particle collision process is implemented through the BGK collision operator. The specific details of performing the BGK collision are existing technologies and will not be elaborated here. The distribution function after the collision is as follows: In the formula, The distribution function after the collision. The distribution function, For the index of discrete velocity directions, The horizontal coordinates of the spatial location Indicates a moment in time. For relaxation frequency, For lattice kinematic viscosity, The equilibrium distribution function; In real-time fluid simulation calculations, an 8×8 thread block configuration is used to balance resource consumption and concurrency. An early exit strategy is employed to eliminate branch divergence. The equilibrium calculation is fully expanded to facilitate compiler instruction scheduling optimization. The equilibrium distribution function is expanded in a second-order form as follows: In the formula, Let be the equilibrium distribution function. For fluid density, For the first Velocity vectors in each direction, The fluid velocity.

[0033] The macroscopic quantities of fluid density, velocity, and curl are obtained by moment calculation of the distribution function. The specific details of the macroscopic quantities obtained by moment calculation are existing technologies and will not be elaborated here.

[0034] A structured array memory layout is used to optimize GPU merged access. Specifically, the distribution functions in nine directions, macroscopic quantities, and temporary storage required for migration are stored in contiguous memory regions. This allows threads within the same warp to access contiguous memory addresses, achieving merged memory access and significantly reducing the number of memory transactions. The formula for calculating the memory address is: In the formula, For the final one-dimensional linear memory index, For the first The initial offset of each physical field For the column index of the current grid, For the row index of the current grid, This is the grid width; The design employs a two-stage Pull-CopyBack migration strategy to avoid data races. Specifically, it transforms the "push" mode in the traditional lattice Boltzmann method migration steps into a "pull" mode. In the pull phase of the pull-copy-back-to-origin mode, each thread reads the collision-triggered distribution function from the upstream position and writes it to a temporary buffer: In the formula, For the temporary buffer distribution function, For write operations, The distribution function after the collision of the upstream lattice; In the copy-to-origin phase of the pull-copy-to-origin mode, the data in the temporary buffer is copied back to the main buffer: In the formula, The distribution function of the main buffer; A two-stage Pull-CopyBack migration strategy is adopted to convert the push mode to a pull mode, fundamentally avoiding write conflicts. Details are attached. Figure 2 As shown, in the Pull phase, each thread is responsible for one grid cell, reading the distribution function after a collision from the upstream position and writing it to a temporary buffer. Since each thread only writes to its own responsible grid cell, there are no write conflicts. The CopyBack phase copies the data from the temporary buffer back to the main buffer, completing the migration process. Although this two-phase strategy adds an extra memory copy, it avoids the serialization overhead of atomic operations, fundamentally avoiding write conflicts without the need for atomic operations.

[0035] The serial scheduling mode of multi-core hypervisors introduces additional scheduling overhead and synchronization waits, which is not the optimal paradigm for GPU parallel computing. However, the collision, migration, and bounce steps in the LBM algorithm have strict data dependencies, making full parallelization impossible while ensuring correctness. Furthermore, if the migration step is completed within a single core hypervisor, concurrent reads and writes to adjacent grid points can lead to data contention. This scheme splits the migration into two stages: Pull (pulling to a temporary buffer) and CopyBack (writing back to the main buffer). Implicit synchronization acts as a barrier, ensuring data consistency and facilitating force computation.

[0036] When performing obstacle bounce calculations, a push-type bounce boundary condition is used. The obstacle element actively pushes the bounced distribution function to the adjacent fluid element, where the bounce rule is as follows: In the formula, Let be the fluid-side distribution function. Let be the fractional function on the obstacle side, where for The opposite direction; this allows each obstacle unit to handle the bounce logic independently, enabling fully parallel processing of obstacle bounces.

[0037] When calculating vorticity, the central difference scheme is used, and the formula for calculating vorticity is: In the formula, vorticity, The horizontal coordinates of the spatial location The vertical coordinates of the spatial location. The velocity component is in the x-axis direction. The velocity component is in the y-axis direction. To perform the partial derivative operation; In force calculations, a force calculation model for obstacles is constructed based on the principle of momentum exchange. When fluid flows over a fixed obstacle, fluid particles collide with and rebound on the obstacle's surface, causing a change in fluid momentum. According to Newton's third law, the change in fluid momentum is equal to the force exerted by the obstacle on the fluid, and its reaction force is the force exerted by the fluid on the obstacle. The formula for calculating the force on fluid particles in a lattice unit is as follows: In the formula, The total force exerted by the fluid on the obstacle. The distribution function pointing towards the obstacle; Specifically, when performing force calculations, the summation iterates through all directions pointing inwards from the obstacle, and the result is expanded into component form: In the formula, The component of force (resistance) in the X-axis direction. The component of force (lift) is in the Y-axis direction. The distribution function is eastward. The distribution function is in the northeast direction. It is a southeast-oriented distribution function. The westward distribution function is... The distribution function is in the northwest direction. It is a southwest distribution function. The northward distribution function, This is the southward distribution function; The calculated force conversion from lattice units to physical units is based on dimensional analysis: In the formula, The original physical forces for fluid simulation calculations. For fluid density, For grid spacing, For time step, This refers to the depth of immersion in water.

[0038] The fluid image is rendered based on the fluid simulation calculation results. When rendering the fluid image, a visual graphics engine such as Unity, Unreal Engine, OpenGL / Vulkan can be used to perform visual rendering based on the various results of the fluid simulation calculation to obtain the fluid image. The rendered fluid image is a 60fps video image.

[0039] When rendering fluid images, a differentiated color mapping algorithm selects different color schemes for different types of scalars. A unified 400-level pseudo-color mapping transforms the flow field scalars into an intuitive color distribution. Figure 3-7 As shown, a piecewise linear interpolation blue-green-yellow-red heatmap scheme is used for unipolar scalars (density, velocity magnitude, curl); a blue-white-red divergent color scheme is used for bipolar scalars (x / y velocity components) to enhance the visual contrast between positive and negative value regions.

[0040] S3. Calculating the gain-based tactile force of fluids based on Reynolds number; the amplitude of the physical unit force calculated using the lattice Boltzmann method is typically only on the order of 0.01-0.1 N. When this small force amplitude is directly mapped to the force feedback device, the user's perception of the force feedback is weak. To enable the user to clearly perceive the fluid dynamics characteristics, the physical force must be amplified. Therefore, this solution introduces a dynamic noise component based on the Reynolds number on top of the global gain coefficient, specifically including the following steps: S301. Calculate the Reynolds number mixing factor based on the Reynolds number. The Reynolds number mixing factor is used to control the transition from laminar to turbulent flow. The Reynolds number mixing factor is calculated using a smooth step function. In the formula, For smooth step functions, The minimum Reynolds number is preferably 40 in this embodiment. The minimum Reynolds number is preferred; in this embodiment, the maximum Reynolds number is 2000. When the Reynolds number is less than the minimum Reynolds number... At this point, the gain force signal degenerates into a pure physical force output, which conforms to the stable characteristics of laminar flow; when the Reynolds number is greater than the maximum Reynolds number, The turbulence fully develops into violent fluctuations; when the Reynolds number is within the range of the minimum and maximum Reynolds number, that is, when the Reynolds number is greater than or equal to the minimum Reynolds number and less than or equal to the maximum Reynolds number, this is within the transition range. Smooth interpolation enables a continuous transition from laminar to turbulent flow.

[0041] S302. Calculate high-frequency noise and low-frequency noise using the phase accumulation method; specifically, this includes the following steps: A1. Calculate the frequencies of high-frequency noise and low-frequency noise: In the formula, The high-frequency noise frequency is calculated based on the Reynolds number difference. For interpolation functions such as SmoothStep, This is the preset lower limit for high-frequency microscale noise. The preset value is the upper limit of the high-frequency microscale noise frequency. The low-frequency noise frequency is calculated based on the Reynolds number difference. The preset limit is the lower limit for low-frequency, large-scale noise. The preset low-frequency large-scale noise limit is set; in this embodiment, the high-frequency noise frequency increases from 10Hz to 50Hz to simulate high-frequency turbulence dissipation; the low-frequency noise component increases from 0.5Hz to 5Hz to simulate wake oscillation.

[0042] A2. The phase of high-frequency noise is calculated based on its frequency, and the phase of low-frequency noise is calculated based on its frequency. To achieve smooth frequency changes and avoid abrupt signal changes, this embodiment uses phase accumulation to generate noise. The update calculation formulas for the phases of high-frequency and low-frequency noise are as follows: In the formula, In order to be in High-frequency noise phase at time, In order to be in High-frequency noise phase at time, The time step is the time interval between two force feedback events. exist Low-frequency noise phase at time, In order to be in The low-frequency noise phase at any given moment; A3. High-frequency noise is generated based on the phase of high-frequency noise, and low-frequency noise is generated based on the phase of low-frequency noise. Specifically, the updated noise phase is normalized to the [-1,1] interval using the Perlin Noise function. To ensure the statistical independence of micro-tremors and macro-surges in the time domain and to avoid artificial periodic overlap, the system calculates the high-frequency noise component and the low-frequency noise component separately. The specific calculation formula is as follows: In the formula, It is high-frequency noise. This is the Berlin noise generation function, whose output range is [0,1]. This is a preset fixed spatial high-frequency sampling offset. It is low-frequency noise. The preset fixed spatial low-frequency sampling offset is used to set different sampling offsets for high-frequency noise and low-frequency noise. This is used to stagger the sampling positions in the Burmester noise space, so that the high-frequency noise and low-frequency noise outputs are completely decoupled random pulsating signals. This ensures that the forces in the two directions are statistically decoupled, avoids artificially generated strong correlations, and thus more realistically restores the pulsating characteristics of fluid anisotropy.

[0043] S303. Obtain the global gain coefficient and calculate the fluid's gain lift and gain drag based on the global gain coefficient, high-frequency noise, and low-frequency noise. When obtaining the global gain coefficient, the user can input it into the computer platform via a keyboard, touchscreen, or other human-computer interaction device. The computer platform then calculates the fluid's gain lift and gain drag based on the user-input global gain coefficient. The specific formula for calculating the gain lift is as follows: In the formula, To increase lift, The global gain coefficient for lift. The original lift force of the fluid obtained from the simulation, The Reynolds number mixing factor, It is high-frequency noise. The high-frequency noise intensity coefficient is preferred in this embodiment. , It is low-frequency noise. The preferred low-frequency noise intensity coefficient is that in this embodiment... The low-frequency noise intensity coefficient and the high-frequency microscale seismic noise intensity coefficient are used to control the relative contribution of the two types of noise. The formula for calculating gain resistance is: In the formula, Gain resistance, The global gain coefficient for resistance. The original fluid resistance obtained from the simulation; In the calculation formulas for gain lift and gain drag, by setting global gain coefficients for lift and drag separately, users can freely adjust the global gain coefficients for lift and drag when setting the gain drag coefficients to separately perceive the lift and drag of the fluid. Furthermore, by setting... and This ensures that the intensity of the pulsation is coupled with the current force scale (i.e., there is no noise when there is no force at rest).

[0044] S304. Calculate the gain tactile force based on the gain lift and gain drag. Specifically, the lift and drag of the fluid obtained in the fluid simulation process are amplified to obtain gain lift and gain drag. The direction vectors of gain lift and gain drag are perpendicular to each other. According to the force composition formula, the gain lift and gain drag are combined into a resultant force to obtain the gain tactile force. The specific content of synthesizing gain lift and gain drag according to the force composition formula is existing technology and will not be elaborated here.

[0045] Traditional linear amplification methods directly amplify the tactile force obtained from fluid simulations using a fixed gain coefficient. While simple, computationally inexpensive, and stable, this approach has inherent limitations. The amplified tactile force is decoupled from the flow physics. Regardless of whether the flow field is in laminar, transition, or turbulent regions, the tactile feedback only reflects amplitude differences, with its time-frequency characteristics remaining unchanged. This prevents users from distinguishing fluid morphology differences at different Reynolds numbers through touch, weakening the effectiveness of embodied cognition in fluid mechanics education.

[0046] In this scheme, the Reynolds number determines the relative dominance of fluid inertial and viscous forces, directly corresponding to the phase transition between laminar and turbulent flow. Furthermore, considering that real turbulence contains multi-scale vortex structures, as the Reynolds number increases, the flow field exhibits both mid-to-low frequency large-scale oscillations corresponding to the shedding of the Karman vortex street and high-frequency small-scale jitters corresponding to boundary layer separation. Moreover, the human tactile system (Pacinian corpuscles et al.) is highly sensitive to vibrations in the 10-500 Hz range and can effectively distinguish the physical characteristics of frequency superposition within this range. Therefore, the force gain method in this scheme is designed. While retaining the global gain coefficient, a Reynolds number-based pulsating component is introduced, and a smooth step function is used to smoothly map the transition state from laminar (Re<40) to turbulent (Re>2000). Simultaneously, dual noise channels—high-frequency micro-scale (10~50 Hz) and low-frequency large-scale (0.5~5 Hz)—are superimposed, dynamically evolving with the Reynolds number to simulate the multi-scale pulsating characteristics of real turbulence, allowing users to perceive the flow regime differences caused by changes in the Reynolds number through touch.

[0047] S4. Send the amplified haptic force to the interaction unit, which outputs haptic force feedback of the fluid based on the amplified haptic force. The specific interaction unit accesses the force feedback device directly in the MonoBehaviour script through the C# interface provided by Haptics Direct for Unity. The plugin provides the HapticPlugin class for device initialization and connection management, as well as a simple interface for constant force output. The Unity main thread normalizes the calculated physical unit force vector and sets the direction and magnitude of the force, then outputs it through the force feedback device. The force feedback device can be 3D Systems Touch, Novint Falcon, Haption Virtuose, etc. The specific usage and driving method of the force feedback device are existing technologies and will not be elaborated here.

[0048] In this embodiment, the teaching effectiveness of the system was verified through a user-controlled experiment. Twenty-four university students without a background in fluid mechanics were recruited and randomly divided into a tactile enhancement group (n=12, using the complete system) and a pure visual group (n=12, force feedback device disabled). The learning effect data are shown in Table 1. Table 1 Summary of Learning Outcome Data Table 1 shows that the force feedback-based fluid field visualization interaction method in this embodiment significantly improves learning effectiveness: the tactile group's learning gain is 47.1% higher than the pure visual group, and the effect size d=0.997 is close to the large effect threshold (d≥0.8). This indicates that force tactile feedback can significantly improve the learning effect of fluid mechanics concepts. The specific mechanism is that tactile feedback, through embodied cognition, transforms abstract mechanical concepts into directly perceptible experiences, enabling learners to understand flow field characteristics simultaneously through both visual and tactile channels.

[0049] The cognitive load data during the learning process are shown in Table 2: Table 2 Cognitive Load Data Table 2 shows that cognitive load did not increase during the learning process: tactile feedback did not significantly increase cognitive burden, but rather slightly reduced it. This challenges the simple assumption that "multimodal learning inevitably increases cognitive load," indicating that well-designed tactile feedback can work in conjunction with visual information to optimize the allocation of cognitive resources by sharing the information processing burden of the visual channel.

[0050] The usability score of this solution is shown in Table 3: Table 3. Distribution of SUS Usability Scores Table 3 shows that the force feedback-based fluid field visualization interaction method of this solution has good user acceptance: the average SUS usability score is 69.58±21.05 (exceeding the acceptable threshold of 68 points), and the proportion of excellent reviews (≥80 points) is 50%. User feedback excerpts: "Being able to see and feel simultaneously leads to a deeper understanding"; "When feeling lift alone, the 'jumping' sensation is very obvious"; "The addition of the tactile dimension provides an additional feedback channel."

[0051] This invention also aims to provide a fluid field visualization and interactive system with force feedback, as shown in the attached figure. Figure 8 As shown, the fluid field visualization interaction method described above includes a fluid calculation unit and an interaction unit; wherein the fluid calculation unit is used to execute the steps of the fluid field visualization interaction method described above; The fluid parameter conversion module is used to convert the input fluid physical parameters into fluid lattice unit parameters; The fluid simulation calculation module is used to perform fluid simulation calculations based on the parameters of the fluid lattice unit. The fluid rendering module is used to render fluids based on the results of fluid simulation calculations.

[0052] The interactive unit includes a fluid visualization module and a tactile sensing module. The fluid visualization module includes an information display panel, an interactive control panel, and a guidance panel. Specifically, the fluid visualization module is an image display device; preferably, in this embodiment, the fluid visualization module is a display screen, as shown in the attached figure. Figure 9 As shown, the various modules in the fluid visualization module are arranged sequentially in the image display device; the information display module is used to display the scene information, parameter information, real-time force information and fluid images of the fluid based on the calculation and rendering results of the fluid simulation calculation unit and the fluid rendering unit; the information display module is read-only to avoid information overload.

[0053] The interactive control panel is used to adjust the adjustable parameters and gain coefficient of the fluid. The various adjustable parameters are interacted with through sliders or selection boxes. When performing interactive control, users can use input devices such as touch screens, mice, or keyboards to adjust the various parameters of the interactive control panel. The specific content of adjusting the various parameters in the interactive control panel is existing technology and will not be described in detail here.

[0054] The guidance section provides concise explanations of core fluid mechanics concepts and outputs real-time verification feedback for various parameters, facilitating guided learning of fluid mechanics.

[0055] The tactile sensing module is used to output tactile force feedback of the fluid based on the rendering results of the fluid rendering unit. The tactile sensing module provides tactile force feedback to the fluid through a force feedback device, which can be a device such as 3D SystemsTouch, Novint Falcon, or Haption Virtuose. The specific structure and force feedback content of the force feedback device are existing technologies and will not be described in detail here.

[0056] When outputting tactile force feedback of the fluid through a force feedback device, this solution uses a 1000Hz physical update frequency to call the fluid simulation calculation unit for fluid simulation calculations. To optimize the allocation of computing resources, as shown in the attached... Figure 10 As shown, this scheme designs an adaptive time step control based on the tactile interaction state. The fluid computing unit dynamically switches the computing mode by monitoring the motion state of the force feedback device in real time, specifically including: In the high-precision haptic mode, when the rate of change of the haptic sensing module's position exceeds a threshold, the fluid computing unit updates the force feedback at a first update frequency of 1000Hz. Specifically, when the system detects that the user is holding and operating the force feedback device, it sets the force feedback update frequency to 1000Hz. In this mode, the fluid simulation calculation module is invoked and fluid simulation calculations are performed every 1ms to ensure that the user perceives subtle changes in fluid force. When determining whether the force feedback device is being held or operated, the system uses the rate of change of the force feedback device's position as the criterion. Specifically, if the rate of change of the force feedback device's position exceeds a threshold, the device is being held and operated; otherwise, the force feedback device is not being held or operated. In this embodiment, the threshold for the rate of change of position is 0.005m / s.

[0057] In the energy-saving visual mode, when the tactile sensing module remains stationary for a period exceeding a stationary time threshold, the fluid calculation unit updates the force feedback at a second update frequency of 100Hz. The stationary time threshold is 0.5 seconds. Specifically, when the force feedback device remains stationary for a period exceeding the stationary time threshold, the system automatically switches to calling the fluid simulation calculation module once every 10ms but performing 10 consecutive fluid simulation calculations, reducing the force feedback frequency to 100Hz. Since the total frequency of fluid simulation calculations is the same in both modes (1000 times / second), the flow field evolution speed remains visually consistent.

[0058] When determining whether the force feedback device is being held and operated or stationary, the position of the force feedback device is sampled every frame through the HapticPlugin interface of the Unity platform, and the rate of change of position is calculated as the interaction state criterion. The specific content of monitoring the force feedback device is existing technology and will not be elaborated here.

[0059] A 3-frame linear interpolation strategy is used when switching between high-precision haptic mode and energy-saving visual mode to avoid haptic jumps caused by sudden changes in force signals.

[0060] This solution reduces the frequency of simulation computing units by 90% (1000Hz → 100Hz) when the user is only visually observing, by using an adaptive time-step adjustment mechanism. This reduces the CPU scheduling burden and frees up computing resources for visualization rendering. Real-world testing data shows that in energy-saving mode, GPU utilization drops from 55% to 27%, and the frame rate increases from a stable 60fps to 123fps, while maintaining a lossless haptic interaction experience.

[0061] The present invention also aims to provide a fluid field visualization and interactive device with force feedback, comprising a memory, a processor, a computer program stored in the memory, and an interactive device, wherein the processor executes the computer program to implement the steps of the above-described fluid field visualization and interactive method with force feedback, and the interactive device is used to provide fluid field visualization and interactive with force feedback based on the processor execution result.

[0062] The present invention also aims to provide a computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, and when the computer program is executed by one or more processors, implements the above-described method for visualizing and interacting with a fluid field with force feedback.

[0063] The present invention also aims to provide a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described fluid field visualization and interaction method with force feedback.

[0064] The present invention also aims to provide an electronic device, including at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the above-described fluid field visualization and interaction method with force feedback.

[0065] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A fluid field visualization and interactive method with force feedback, characterized in that, Includes the following steps: Obtain the fluid physical parameters of the target fluid scene, convert the fluid physical parameters into fluid lattice unit parameters, and calculate the Reynolds number based on the fluid physical parameters and fluid lattice unit parameters; Fluid simulation calculations are performed based on the parameters of the fluid lattice unit, and fluid images are rendered based on the simulation results. The gain tactile force of the fluid is calculated based on the Reynolds number and fluid simulation results; Amplified tactile force is sent to an interactive unit, which outputs force tactile feedback of the fluid based on the amplified tactile force.

2. The fluid field visualization and interactive method according to claim 1, characterized in that, The gain tactile force of the fluid calculated based on Reynolds number and fluid simulation results includes: Calculate the Reynolds number mixing factor based on the Reynolds number; Calculate high-frequency noise and low-frequency noise based on the Reynolds number mixing factor; Obtain the global gain coefficient, and calculate the gain lift and gain drag of the fluid based on the global gain coefficient, high-frequency noise, and low-frequency noise; Gain tactile force is calculated based on gain lift and gain drag.

3. The fluid field visualization and interactive method according to claim 2, characterized in that, The calculation of high-frequency noise and low-frequency noise based on the Reynolds number mixing factor includes: Calculate the frequencies of high-frequency noise and low-frequency noise based on the Reynolds number mixing factor; Calculate the phase of high-frequency noise based on its frequency, and calculate the phase of low-frequency noise based on its frequency. High-frequency noise is generated based on the phase of high-frequency noise, and low-frequency noise is generated based on the phase of low-frequency noise.

4. The fluid field visualization and interactive method according to claim 2, characterized in that, The formula for calculating the lift gain of the fluid is: In the formula, To increase lift, The global gain coefficient for lift. The original lift force of the fluid obtained from the simulation, The Reynolds number mixing factor, It is high-frequency noise. This is the high-frequency noise intensity coefficient. It is low-frequency noise. This refers to the low-frequency noise intensity coefficient. The formula for calculating the gain resistance of the fluid is: In the formula, Gain resistance, The global gain coefficient for resistance. The original fluid resistance is obtained from the simulation.

5. The fluid field visualization and interactive method according to claim 1, characterized in that, The migration strategy for fluid simulation calculation based on fluid lattice unit parameters is a pull-copy back-to-source mode. In the pull phase of the pull-copy back-to-source mode, the distribution function of the fluid simulation calculation is obtained and written into a temporary buffer. In the copy back-to-source phase of the pull-copy back-to-source mode, the data in the temporary buffer is copied back to the main buffer.

6. A fluid field visualization and interactive system with force feedback, characterized in that, Includes a fluid computing unit and an interaction unit; The fluid computing unit is used to perform the steps of the fluid field visualization and interaction method as described in any one of claims 1-5; The interaction unit is used to provide human-computer interaction based on the execution results of the fluid computing unit.

7. The fluid field visualization and interactive system according to claim 6, characterized in that, The interactive unit includes a fluid visualization module and a tactile perception module. The fluid visualization module is used to provide fluid visual interaction, and the tactile perception module is used to provide force tactile feedback interaction based on the fluid rendering results.

8. The fluid field visualization and interactive system according to claim 7, characterized in that, The fluid computing unit is used to switch computing modes according to the motion state of the tactile sensing module, and the computing modes include: In the high-precision tactile mode, when the position change rate of the tactile sensing module is greater than the position change rate threshold, the fluid computing unit performs force feedback updates at the first update frequency. In the energy-saving vision mode, when the tactile sensing module remains stationary for a period of time longer than the stationary time threshold, the fluid computing unit updates the force feedback at a second update frequency.

9. A fluid field visualization and interactive device with force feedback, comprising a memory, a processor, a computer program stored in the memory, and an interactive device, characterized in that, The processor executes the computer program to implement the steps of the fluid field visualization interaction method with force feedback as described in any one of claims 1-5, wherein the interaction device is used to provide fluid field visualization interaction with force feedback based on the processor execution result.

10. A computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, characterized in that, When the computer program is executed by one or more processors, it implements the fluid field visualization and interactive method with force feedback as described in any one of claims 1-5.

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