Method for simulating the flow of a fluid in a volume surrounding a component of a vehicle or technical system using initial velocities determined by a physically informed neural network as starting values ​​for the simulation.

Abstract

The invention relates to a control system (1) with a computer system (20) for simulating a flow (3) of a fluid in a volume (6) surrounding a component of a vehicle, wherein a shape of the volume (6) is specified by values ​​of geometric parameters and the computer system (20) is configured to iteratively determine velocities of the fluid in the regions of the volume (6) depending on boundary conditions for the flow (3) of the fluid at the edges of the volume (6) and initial velocities of the fluid in regions of the volume (6), wherein the iteratively determined velocities describe the flow (3) and the computer system (20) comprises a physically informed neural network (PINN) (22) which is trained on the results of simulations of fluid flows, and the computer system (20) is configuredto determine the initial velocities of the fluid in the areas using the PINN (22) as a function of the boundary conditions and the values ​​of the geometric parameters, and the control system (1) is set up to control at least one component of the vehicle as a function of the iteratively determined velocities.

Description

[0001] The invention relates to a computer system for simulating the flow of a fluid in a volume surrounding a component of a vehicle or a technical system, a control system for controlling a component of the vehicle depending on velocities of the fluid determined iteratively by the simulation, and a method for simulating the flow of a fluid in a volume surrounding a component of a vehicle or a technical system.

[0002] It is known to simulate fluid flows, for example, around parts of a vehicle. Simulating such flows often requires a very high level of computing power, usually with the aid of supercomputers. In most cases, the computational effort depends on knowledge of the initial velocity field of the flow. The more accurately this initial velocity field can be approximated, the lower the computational effort required to calculate the flow is generally.

[0003] A control system is proposed that includes a computer system for simulating the flow of a fluid within a component of a surrounding volume. The shape of the volume is specified by values ​​of geometric parameters. The computer system is configured to iteratively determine fluid velocities in specific regions of the volume, depending on boundary conditions for the fluid flow at the volume's edges and initial fluid velocities within those regions. These iteratively determined velocities describe the flow. The determination of these velocities can be considered a flow simulation.

[0004] The computer system incorporates a physically informed neural network (PINN) trained on the results of fluid flow simulations. Furthermore, the computer system is configured to determine the initial fluid velocities in the relevant areas using the PINN, based on boundary conditions and geometric parameters. The control system is then configured to steer at least one vehicle component according to these iteratively determined velocities.

[0005] Furthermore, a computer system for simulating fluid flow within a volume surrounding a component of a vehicle or technical system is proposed. The shape of the volume is specified by values ​​of geometric parameters. The computer system is configured to iteratively determine fluid velocities in specific regions of the volume, based on boundary conditions for fluid flow at the volume's edges and initial fluid velocities within those regions. These iteratively determined velocities describe the flow. The computer system incorporates a physically informed neural network (PINN). The PINN is trained using results from fluid flow simulations. The computer system is further configured to use the PINN to determine the initial fluid velocities in these regions, based on the boundary conditions and the values ​​of the geometric parameters.

[0006] Furthermore, a method for simulating the flow of a fluid in a volume surrounding a component of a vehicle or technical system is proposed. The method involves determining initial fluid velocities in regions of the volume using a physically informed neural network (PINN) as a function of boundary conditions for the fluid flow at the volume boundaries and values ​​of geometric parameters. The shape of the volume is specified by the values ​​of the geometric parameters, and the PINN is trained using results from fluid flow simulations. The method further includes iteratively determining fluid velocities in these regions of the volume as a function of the boundary conditions and the initial fluid velocities. The iteratively determined velocities then describe the flow.

[0007] Furthermore, a computer program product is proposed with instructions executable by one or more processors, wherein the execution of the instructions causes the processors to carry out the procedure.

[0008] The iteratively determined fluid velocities are referred to simply as velocities in the following. The iterative determination of fluid velocities described above can involve iteratively solving a system of equations to determine the fluid velocities. For example, the computer system can be configured to perform multiple iterations to solve the system of equations and determine the fluid velocities as a function of the solved equations.

[0009] Conveniently, the computer system is configured to perform a first iteration to solve the system of equations based on the initial fluid velocities. For example, the computer system can be configured to input the initial velocities into the system of equations and perform the first iteration to determine a first approximate solution. Furthermore, the computer system can be configured to perform one or more additional iterations based on this first approximate solution to determine further approximate solutions to the system of equations.

[0010] Performing the first and / or subsequent iterations may each involve calculating preliminary velocities in the regions and correction values ​​for these preliminary velocities. The regions are generally configured such that, collectively, they represent the volume. In other words, the volume is divided into these regions.

[0011] The computer system can be configured to determine the preliminary velocities as a function of the initial velocities during the first iteration. Furthermore, the computer system can be configured to determine the correction values ​​as a function of the preliminary velocities. Finally, the computer system can be configured to determine the fluid velocities as a function of the preliminary velocities and / or the correction values ​​from the last iteration. In this case, the velocities are determined indirectly by performing the first or subsequent iterations as a function of the initial velocities.

[0012] By configuring the computer system to determine the fluid velocities based on the fluid's initial velocities, and by making the fluid's initial velocities determinable using PINN, the iterative determination of the velocities could be accelerated, particularly by reducing the number of iterations required to solve the system of equations. This could, firstly, reduce the computation time needed to determine the velocities describing the flow. Alternatively or additionally, it could reduce the requirement for the computer system to simulate the flow, such as the number of processors needed for iteratively solving the system of equations.

[0013] Reducing computation time and / or requirements can be particularly relevant in applications where a specific accuracy is required when solving a system of equations. The required accuracy is often specified as a predetermined limit on the residual of the equation system. By configuring the computer system to iteratively determine the velocities based on the initial fluid velocities, and by determining these initial velocities using PINN, the number of iterations required for the iterative calculation of the velocities could be reduced, provided that the residual of the equation system remains below the predetermined limit.

[0014] Reducing computation time could significantly increase the number of different possible component shapes that can be investigated using flow simulation. For example, instead of 10 to 50 different shapes, up to 10,000 possible shapes could be examined during a single component development phase. The computer system can be configured to repeatedly run the flow simulation, changing the component shape with each iteration. This allows the computer system to be used for the design of components for vehicles or technical systems.

[0015] If the component is a vehicle part, the volume surrounding it can, according to one variant, enclose several vehicle parts, in particular several parts of the vehicle's outer body skin. The vehicle's outer skin can form a first boundary surface of the volume. A second boundary surface can, for example, be located at a vertical distance from a roadway on which the vehicle is located. This vertical distance can be, for example, 3 meters. Further boundary surfaces of the volume can, for example, extend in front of the vehicle at a first horizontal distance and behind the vehicle at a second horizontal distance. The first horizontal distance can be, for example, 5 to 10 meters and the second horizontal distance 10 to 20 meters.

[0016] According to another application, the volume surrounding the vehicle part can surround an inner surface of the vehicle part. For example, the vehicle part can be designed in the form of a diffuser, and the surrounding volume can be bounded by an inner surface of the diffuser.

[0017] This is not to be understood as a limitation. The component, whether a vehicle part or part of a technical system, can be a compressor, turbine, nozzle, guide vane, pump impeller, or other component that is surrounded or through which a fluid flows. In the case of a nozzle, the surrounding volume can enclose an inner surface of the nozzle along which the fluid flows.

[0018] The technical system could be, for example, an energy or power plant, a plant in the chemical process industry, part of a building climate control system, a water treatment plant, etc. Likewise, the vehicle need not be a passenger car. The invention can also be applied to other types of vehicles where the flow of a fluid plays a role, such as motorcycles, airplanes, helicopters, drones, and other vehicles.

[0019] According to one approach, the shape of a volume can be described by its boundary surfaces. In this case, the values ​​of the geometric parameters can specify points on the boundary surfaces of the volume. These geometric parameter values ​​can be the coordinates of the points lying on the boundary surfaces. Alternatively, the geometric parameter values ​​can specify the coordinates of internal points located within the interior of the volume. In this case, the internal points can be evenly distributed throughout the volume. It is also possible for the geometric parameter values ​​to describe how the internal points are distributed within the volume. Here, the geometric parameter values ​​could, for example, be the parameters of a shape function that defines the distribution of the coordinates of the internal points within the volume.

[0020] The boundary conditions for the flow can include, for example, a predetermined pressure at one of the aforementioned interfaces of the volume, a predetermined fluid velocity, and / or a change in the fluid velocity with respect to location at at least one of the aforementioned interfaces of the volume. The fluid velocities can at least partially describe the flow of the fluid within the volume. In addition to the velocities, the flow can, for example, be described by a specific pressure prevailing in the respective region. The computer system can be configured to determine the pressures in the regions of the volume during the iterative solution of the system of equations, particularly during the final iteration.

[0021] The results of the fluid flow simulations used to train PINN can be generated by simulations of the fluid flow in different additional volumes. It is understood that each fluid flow simulation represents a simulation of the fluid flow in the respective additional volume. The simulation results can be generated using common CFD methods such as the finite volume method (FVM), finite element method (FEM), finite difference method (FDM), and spectral methods to solve the Navier-Stokes equations. To generate the simulation results, the Navier-Stokes equations can be solved in discretized form to model momentum and mass conservation in the additional volumes. For this purpose, each additional volume can be divided into a set of further regions that together represent the respective volume.In principle, turbulence models such as LES, RANS or DNS can also be used to simulate the flow of the fluid in the other volumes.

[0022] The simulation results can include a set of fluid velocities and pressures for each additional volume. The respective velocity and pressure of each set can then be used to determine the fluid velocity and pressure for that specific region within that additional volume.

[0023] The additional volumes can have different shapes, especially differently designed interfaces. The shape of each additional volume can be specified by a specific set of values ​​for the geometric parameters.

[0024] The results of the fluid flow simulations in the other volumes can be generated using a separate computer system. This additional computer system typically has a higher computing capacity, particularly a greater number of CPUs, than the primary computer system. By training the PINN (Personalized Flow Network) using the fluid flow simulation results, physical information about the fluid flow in the different volumes can be stored within the PINN, for example, in the form of stored values ​​for the PINN's weights. The trained PINN could then enable the acquisition of physical information about the fluid flow in the volume surrounding the component, depending on the boundary conditions and the values ​​of the geometric parameters. This physical information could be expressed as the initial fluid velocities.The computer system can use the physical information when executing the first iteration. This would allow a "best possible" starting point for the iterations to be used in the form of the initial fluid velocities, thus reducing the number of iterations.

[0025] The control system can be configured to control the vehicle component directly or indirectly depending on the speeds. A direct approach could, for example, involve calculating an average speed from iteratively determined speeds and controlling the component based on this average speed. An indirect approach to controlling the component based on speeds could, for example, involve calculating the pressure surrounding the component as a function of the speeds and controlling the component based on this pressure.

[0026] The vehicle component could be, for example, a drive system, a braking system, or an aerodynamic component such as a front wing. By reducing the number of iterations using the initial speeds determined with the PINN, the speeds could be determined more quickly, especially in real time, by the computer system. This could enable real-time control of the component based on the speeds. For example, it might be possible to decelerate the vehicle more quickly in response to a changing crosswind or to increase the downforce of the front wing. In this application example, the boundary conditions could specify the direction of the crosswind.

[0027] In one configuration, the computer system can be integrated into the vehicle. Alternatively, the control system can comprise a control unit integrated into the vehicle that connects to a computer system located outside the vehicle, for example, in a cloud. In this case, the control system would include a portion of the cloud that provides the computer system. A first set of boundary conditions, such as information about the shape of a vehicle component, particularly the outer skin, can be sent from the vehicle to the cloud. A second set of boundary conditions, such as the direction of the crosswind, can be sent from an external computer system to the control system. This external computer system could, for example, be configured to perform weather simulations for the area where the vehicle is located.Results from weather simulations can include, for example, the direction of the crosswind.

[0028] Controlling the drive and / or braking systems based on speeds determined by crosswinds could reduce the vehicle's energy consumption, particularly fuel consumption. The underlying principle is that the vehicle's aerodynamic drag is proportional to the square of the relative wind it encounters. By considering the strength and direction of the crosswind, the vehicle's speed can be controlled more energy-efficiently. Controlling the aerodynamic components based on speeds determined by crosswinds could also improve the vehicle's road grip and thus its safety.

[0029] In a further embodiment, the boundary conditions include information about the shape, distance, and / or speed of another vehicle in the vicinity of the vehicle. This other vehicle may be located, for example, in front of, behind, or to the side of the vehicle. Information about the shape of the other vehicle may be provided, for example, by specifying its model type. Information about the distance may be a statement about the relative distance between the other vehicle and the vehicle. Information about the speed of the other vehicle may be provided as its relative speed to the vehicle or as its absolute speed.

[0030] It is understood that the boundary conditions can also include further information about the shapes and / or speeds of other vehicles in the vicinity of the vehicle. Determining the speeds as a function of the boundary conditions, in cases where the boundary conditions include information about the shape and / or speed of the other vehicle, could have the advantage that the fluid flow can be determined as a function of the vehicle's current traffic situation. This could enable even more efficient control of the vehicle's component. The current traffic situation is specified here by the shape, distance, and / or speed of the other vehicle(s).

[0031] In a further embodiment, the computer system is configured to determine the velocities iteratively using the system of equations. This system of equations can comprise a first system describing the conservation of momentum for the volume regions and a second system describing the conservation of mass for the other regions.

[0032] Because the first system of equations can describe the conservation of momentum for the regions of the volume, and the second system of equations can describe the conservation of mass for the regions of the volume, the fluid flow in the volume can be expressed in terms of the Navier-Stokes equation. Describing the fluid flow using the Navier-Stokes equations generally provides the most accurate way to simulate the fluid flow in the volume. However, discretizing the Navier-Stokes equations typically results in very large matrices for describing the first and second systems of equations. Due to these comparatively large matrices, a high number of the aforementioned iterations are usually required to reach the specified bound for the residual.For this reason, it could be particularly advantageous, especially when using the first and second systems of equations, to determine the initial velocities of the fluid using PINN.

[0033] In a further embodiment, the computer system can be configured to perform the SIMPLE (Semi-implicit-Method for Pressure Linked Equations) algorithm for iterative determination of the fluid velocities and, in a first iteration of the SIMPLE algorithm, to determine the preliminary fluid velocities in the regions as a function of the initial velocities.

[0034] In this configuration, the computer system can be set up to correct the preliminary speeds once within the first iteration and, if necessary, once in each subsequent iteration of the SIMPLE algorithm. The initial speeds can be considered a starting value for calculating the preliminary speeds when performing the first iteration of the SIMPLE algorithm. Furthermore, the SIMPLE algorithm typically only performs one pressure correction per iteration. Therefore, depending on the application, the number of iterations required can be very high until the residual falls below the threshold.For this reason, it is particularly advantageous to determine the initial speeds using PINN, especially when the SIMPLE algorithm is applied, since the initial speeds determined in this way represent a good estimate for the speeds in most applications and could thereby reduce the number of iterations.

[0035] In a further embodiment, the computer system can be configured to perform the PISO (Pressure-Implicit with Splitting Operators) algorithm for the iterative determination of the fluid velocities and, in a first iteration of the PISO algorithm, to determine the preliminary fluid velocities in the areas as a function of the initial velocities.

[0036] In this configuration, the computer system can be set up to correct the preliminary speeds several times within the first iteration and, if necessary, in each subsequent iteration of the PISO algorithm. The initial speeds can be considered a starting value for calculating the preliminary speeds when performing the first iteration of the PISO algorithm. Furthermore, a pressure correction is typically performed several times per iteration during the execution of the PISO algorithm.

[0037] The multiple corrections to the preliminary velocities and pressures can be considered inner iterations of the PISO algorithm. The iterations described so far can be considered outer iterations. The number of inner iterations can be very high, depending on the application, until the residual for the inner iterations falls below a further predefined limit. For this reason, it is particularly advantageous to determine the initial velocities using PINN when applying the PISO algorithm, as the initial velocities determined in this way represent a good estimate for the velocities in most applications, and the number of inner iterations could therefore be reduced.

[0038] Preferred embodiments are explained in more detail with reference to the following figures. The dependent claims describe further advantageous embodiments of the invention. The figures schematically illustrate this. Fig. 1. A flow around the body of a vehicle and a control system for the vehicle; Fig. 2 a computer system of the in Fig. 1. Tax system shown; Fig. 3 a computing area divided into several areas for calculating the in Fig. 1. Flow shown; Fig. 4 a first further computational area for calculating a first further flow around a first further object; Fig. 5 a second further computational area for calculating a second further flow around a second further object.

[0039] Fig. Figure 1 shows a control system 1, which is in Fig. 2 Computer system 20 shown for simulating a flow 3 of a fluid in a volume 6 surrounding a vehicle part 4 of a vehicle 5. The flow 3 is in Fig. 1 schematically represented using arrows. Vehicle part 4 can be seen in the Fig. In the application shown in Figure 1, the upper surface of a vehicle body skin 5 is the upper surface. Conveniently, the control system includes a control unit 2, which is configured to control at least one component of the vehicle 5 depending on the fluid velocities in regions 30 of the volume 6, which are iteratively determined by the computer system 20. The component of the vehicle 5 can, for example, be a drive system 7, a braking system 8, or a front wing of the vehicle 5 (not shown in the figures).

[0040] According to one variant not explicitly shown in the figures, the computer system 20 can be integrated into the vehicle 5. According to an alternative embodiment, the computer system 20 can be located externally from the vehicle 5, for example in a cloud. In this embodiment, the control unit 2 can be configured to establish a communication link, such as a radio link, to the computer system 20.

[0041] Volume 6 can be, as in Fig. Figure 3 shows that the areas 30 are divided into such a way that the areas 30 together completely represent the volume 6. The shape of the volume 6 can be specified by values ​​of geometric parameters. Furthermore, the volume 6 can be described by a description of the location and / or shape of the boundaries of the volume 6 or the location of internal points of the volume 6. For the sake of simplicity, the volume 6 is shown two-dimensionally in the figures. However, it is understood that the volume 6 extends in three dimensions. For the in Fig. In the application shown in 1, a first edge 11 of the volume 6 can be located in front of the vehicle 5 and perpendicular to a surface not in the Fig. The first edge of volume 6 extends along the roadway shown in Figure 1, on which the vehicle 5 is located. A second edge 12 of volume 6 can extend above the vehicle 5 and parallel to the roadway at a distance from the roadway. A third edge 13 of volume 6 can extend behind the vehicle 5 and perpendicular to the roadway. A fourth edge 14 can initially extend parallel to the roadway and then along the top surface of the vehicle's outer skin. Following this, the fourth edge 14 can again run parallel to the roadway.

[0042] The shape of volume 6 can be specified by values ​​of geometric parameters. For example, the course of the fourth edge 14 in a region where the fourth edge 14 runs along the body's outer skin can be described by coordinates of points 140 that approximate a shape of the top surface of the body's outer skin.

[0043] Computer system 20 is configured to iteratively determine the fluid velocities in the regions 30 of volume 6, depending on boundary conditions for the fluid flow 3 at the boundaries 11, 12, 13, 14 of volume 6 and initial fluid velocities in the regions 30 of volume 6. For this purpose, computer system 20 can be configured to perform the simulation of the fluid flow 3 in volume 6 by executing program code stored in a memory of computer system 20. The program code can include a simulation module 21 for performing the aforementioned first iteration and, if necessary, for performing the aforementioned further iterations.

[0044] The regions 30 can be configured as hexahedra, tetrahedra, prisms, pyramids, and / or polyhedra if the volume 6 is represented by a three-dimensional computational domain during the simulation. For example, within the volume 6, the regions 30 can be constructed as hexahedra. Along the fourth boundary 14, some of the regions 30 can be configured as polyhedra to approximate the shape of the fourth boundary 14 to a shape of the vehicle's outer skin. For clarity, not all regions 30 are shown in Fig. 3 is marked with a reference symbol. The three-dimensional computational domain has the same proportions as the volume 6. The areas 30 of the in Fig. The volume 6 represented in Figure 3 can therefore be understood as regions of the computational domain. If the volume 6 is represented by a two-dimensional computational domain, the regions 30 can be shaped as cuboids, rectangles, or triangles. In this case, the flow simulation 3 can be performed as a 2D flow simulation.

[0045] The velocities can be considered part of the simulation result. The simulation result typically includes a set of fluid velocity values ​​assigned to each region (30). This set includes fluid velocity values ​​in three spatial directions if the volume (6) is represented by a three-dimensional computational domain. If the volume (6) is represented by a two-dimensional computational domain, the set includes velocity values ​​in two directions. In both cases, the three-dimensional and two-dimensional velocities describe the flow (3) at least partially.

[0046] The boundary conditions can, for example, specify a direction of velocity at the first edge 11, the second edge 12, and the third edge 13 that runs parallel to the roadway. Furthermore, the boundary conditions can stipulate that the magnitude of the velocity at the first edge 11 is constant and / or that any change in pressure and / or velocity in a direction perpendicular to the third edge 13 is zero.

[0047] Furthermore, computer system 20 can have a PINN 22 to calculate the initial fluid velocities. The initial velocities can be part of an output 22.2 of PINN 22. PINN 22 can be configured to determine the initial velocities depending on the boundary conditions and the values ​​of the geometric parameters. In this case, PINN 22 is in a trained state. According to one variant, the boundary conditions and the values ​​of the geometric parameters can be read into computer system 20 via an input 20.1 of computer system 20 and thus be processable by computer system 20, in particular PINN 22. The boundary conditions can, for example, be sent to computer system 20 from the aforementioned external computer system. The values ​​of the geometric parameters can be sent to computer system 20 from the control unit 2 if computer system 20 is installed in the cloud.In the event that the computer system 20 is integrated into the vehicle 5, the values ​​of the geometric parameters are conveniently stored in the memory of the computer system 20.

[0048] The PINN 22 is trained using results from further simulations of additional fluid flows. These additional simulations depict the further flows that can develop when the fluid flows around other objects.

[0049] As an example, the shape of a first further object is approximated by first further points 440. Using these first further points 440, the shape of the first further object can be approximated, and thereby a first further lower boundary 40 of a first further volume 6.1 can be specified. Like volume 6, the first further volume 6.1 comprises the first boundary 11, the second boundary 12, and the third boundary 13. A first further simulation of a first further flow can include a calculation of the fluid flow around the first further object, where the Fig.The first additional volume 6.1 shown in Figure 4 is used as the computational domain. The first additional flow is conveniently calculated using a supercomputer and the aforementioned common CFD methods. In one variant, the same boundary conditions used for simulating the fluid flow 3 at boundaries 11, 12, 13, and 14 can be used. Alternatively, other boundary conditions can be used to increase the number of different flows represented by training data for PINN 22.

[0050] Similarly, a second simulation can be performed. This second simulation involves simulating a second fluid flow around a second object, which can be approximated by the second point 540. Based on the second point 540, a second lower boundary 50 of a second volume 6.2 can be defined. Similarly, the second volume 6.2 is used as the computational domain in the second simulation. Conveniently, a number of points 140 is equal to a number of first points 440 and a number of second points 540. This could increase the accuracy of PINN 22 in determining the initial velocities.

[0051] For training PINN 22, input training datasets can be used. These datasets contain the boundary conditions of the respective further simulation and a set of geometric parameter values ​​describing the location of the respective further points, such as points 440 and 540. Output training datasets for PINN 22 can consist of velocities prevalent in regions of the respective further volume, such as further volumes 6.1 and 6.2, according to the results of the respective further simulation. It is understood that each further volume is divided into a set of further regions for the respective further simulation.Analogous to the first and second further simulations, several further simulations can be carried out to increase the amount of training datasets, each comprising the respective input training dataset and the respective output training dataset.

[0052] Parameter values ​​of PINN 22, such as the weights of PINN 22 neurons, can be trained using a loss function. During training, a value of the loss function can be determined based on a residual from another system of equations describing the specific flow. In this variant, the initial training datasets can contain information about the residual. This additional system of equations could, for example, be the one mentioned above. By including the residual in the loss function, physical information, particularly about the Navier-Stokes equations, can be incorporated into the training of PINN 22.

[0053] Computer system 20 can now be configured to route the output 22.2 of PINN 22, in particular the initial velocities, to a second input 21.2 of simulation module 21. Furthermore, computer system 20 can be configured to route the boundary conditions for the flow 3 to a first input 21.1 of simulation module 21. In principle, the values ​​of the geometric parameters that at least partially specify the shape of volume 6, for example, in the form of the coordinates of points 140, can be supplied to simulation module 21 for iterative calculation of the velocities. Alternatively, the values ​​of the geometric parameters can be stored in simulation module 21. Simulation module 21 is configured to output the simulation result as output 21.3. Computer system 20 can output the simulation result via output 20.2.According to one possible configuration, the computer system 20 can be set up to send the result of the simulation, in particular the speeds, to the control unit 2 via output 20.2.

[0054] Simulation module 21 can be configured to iteratively determine the velocities by executing the SIMPLE algorithm. In a first iteration of the SIMPLE algorithm, simulation module 21 can determine preliminary fluid velocities in the regions as a function of the initial velocities by solving the momentum conservation equation according to Equation 1: ρ(u⋅∇u)=−∇p+μ∇2u

[0055] Here, the pressure p is initially estimated. The preliminary velocities are denoted by u in Equation 1 (Eq. 1). Matrices for solving a linear system of equations, derived by linearizing Eq. 1, can be stored in the memory of the computer system 20. The simulation module 21 can be configured to iteratively solve the linearized Eq. 1 using these matrices, for example, using a GMRES (Generalized Minimal Residual Method) solver. Within each iteration of the SIMPLE algorithm, further iterations of the GMRES solver can therefore be performed. The simulation module 21 can be configured to use the initial velocities as starting values ​​in a first iteration when performing the iterative solution of the linearized Eq. 1. In this way, convective terms can be determined as a function of the initial velocities.

[0056] Furthermore, the simulation module 21 can be configured to correct the preliminary velocities by velocity correction values ​​u' and the estimated pressure by pressure correction values ​​p' as follows: u=u*+u' and p=p*+p'

[0057] In Eq. 2, u* denotes the preliminary velocity and u the corrected velocity, and in Eq. 3, p* denotes the estimated pressure and p the corrected pressure.

[0058] The continuity equation ∇·u = 0 can be formulated as follows: ∇⋅(u*+u')=0⇒∇⋅u'=−∇⋅u*

[0059] The correction rate u' is derived from the pressure gradient as follows: u'=−(1 / ap)∇p'

[0060] Substituting equation 5 into equation 4 yields the pressure correction equation: ∇⋅[(1 / ap)∇p']=∇⋅u*

[0061] Simulation module 21 can be configured to determine the pressure correction value p' for the pressure in the respective area 30 according to Eq. 6. Furthermore, simulation module 21 can be configured to update the pressure according to Eq. 7 and the velocity according to Eq. 8 in the respective iteration of the SIMPLE algorithm for the respective area 30. pn+1=p*+αp⋅p' un+1=u*−(1 / ap)∇p'

[0062] A relaxation factor α pThe simulation module 21 can improve the convergence behavior of the SIMPLE algorithm iterations. It can be configured to check, during each iteration of the SIMPLE algorithm, whether a residual of Eq. 1 falls below the specified limit. Depending on the application, the residual may fall below the limit even in the first iteration of the SIMPLE algorithm. This can occur if the initial velocities are approximated sufficiently well using PINN 22, i.e., such that the residual falls below the limit. In this case, a classical convergence criterion can be used with the simulation module 21 to assess the accuracy of the initial velocities.

[0063] In the event that only one iteration of the SIMPLE algorithm is performed, the velocities are usually still determined iteratively as a function of the initial velocities, for example, by using the GMRES solver. If the residual after the first iteration does not yet fall below the bound, the simulation module 21 repeatedly performs the calculations described above according to equations 1 to 8 in a second iteration or further iterations, which are referred to below as outer iterations. The updated velocities can be incorporated into equation 1 via the convective terms of equation 1. For example, in equation 1, ρ(u · ∇u) can be replaced by ρ(u aktualisiert · ∇u) are replaced, where u aktualisiert same u n+1 according to Eq. 8.

[0064] In one variant, simulation module 21 is configured to execute the PISO algorithm. Here, the pressure correction according to Eq. 6 and the updates according to Eqs. 7 and 8 are performed several times in succession, which can be referred to as inner iterations. During the second or nth pressure correction in the PISO algorithm, the pressure correction value p' in Eq. 6 is determined as a function of the updated speeds instead of the preliminary speeds. Under certain circumstances, the outer iterations can be omitted when executing the PISO algorithm.

[0065] In one possible embodiment, the computer system is configured to determine initial fluid pressures in regions 30 using PINN 22, depending on the boundary conditions and the values ​​of the geometric parameters. Based on these initial pressures, the system iteratively determines the fluid velocity in regions 30. The initial pressures can represent the estimated pressure values ​​in the respective region 30. This would further increase the amount of flow information obtainable via PINN 22 and incorporated into the simulation. This, in turn, could further reduce the number of iterations required to reach the residual limit.

[0066] In another variant, the computer system 20 can be configured to generate a residual of the equation system during the iterative determination of the fluid velocities and to evaluate the PINN 22 based on this residual. The equation system can, for example, include the linearized equation Eq. 1, which represents the first equation system mentioned above. In principle, the equation system can also include Eq. 4, which represents the second equation mentioned above. The lower the residual, the better the PINN 22 can approximate the flow 3.

[0067] The term "module," as used herein, describes any known or subsequently developed hardware, software, firmware, artificial intelligence, fuzzy logic, or combination thereof, capable of performing the functionality associated with the respective "module." For example, Simulation Module 21 may comprise a set of instructions to solve one or more of the equations mentioned above.

Claims

[1] Control system (1) comprising a computer system (20) for simulating a flow (3) of a fluid in a volume (6) surrounding a component of a vehicle, wherein a shape of the volume (6) is specified by values ​​of geometric parameters and the computer system (20) is configured to iteratively determine velocities of the fluid in regions of the volume (6) depending on boundary conditions for the flow (3) of the fluid at edges of the volume (6) and initial velocities of the fluid in regions of the volume (6), wherein the iteratively determined velocities describe the flow (3) and the computer system (20) comprises a physically informed neural network (PINN) (22) which is trained on results of simulations of fluid flows, and the computer system (20) is configuredto determine the initial velocities of the fluid in the areas using the PINN (22) as a function of the boundary conditions and the values ​​of the geometric parameters, and the control system (1) is set up to control at least one component of the vehicle as a function of the iteratively determined velocities. [2] Control system (1) according to claim 1, wherein the boundary conditions include information about a shape, distance and / or speed of another vehicle in a vicinity of the vehicle. [3] Computer system (20) for simulating a flow (3) of a fluid in a volume (6) surrounding a component of a vehicle or a technical system, wherein a shape of the volume (6) is specified by values ​​of geometric parameters and the computer system (20) is configured to iteratively determine velocities of the fluid in the regions depending on boundary conditions for the flow (3) of the fluid at the edges of the volume (6) and initial velocities of the fluid in regions of the volume (6), wherein the iteratively determined velocities describe the flow (3) and the computer system (20) comprises a physically informed neural network (PINN) (22) which is trained on results of simulations of fluid flows, and the computer system (20) is configuredto determine the initial velocities of the fluid in the regions using PINN (22) as a function of the boundary conditions and the values ​​of the geometric parameters. [4] Computer system (20) according to claim 3, wherein the computer system (20) is configured to iteratively determine the velocities using a system of equations, wherein the system of equations comprises a first system of equations to describe conservation of momentum for the regions of the volume (6) and a second system of equations to describe conservation of mass for the regions. [5] Computer system (20) according to claim 3 or 4, wherein the computer system (20) is configured to perform the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm for iterative determination of the fluid velocities and in a first iteration of the SIMPLE algorithm to determine preliminary fluid velocities in the regions as a function of the initial velocities. [6] Computer system (20) according to claim 3 or 4, wherein the computer system (20) is configured to perform the PISO (Pressure-Implicit with Splitting Operators) algorithm for iterative determination of the fluid velocities and in a first iteration of the PISO algorithm to determine preliminary fluid velocities in the regions as a function of the initial velocities. [7] Computer system (20) according to any one of the preceding claims 3 to 6, wherein the computer system (20) is configured to determine initial pressures of the fluid in the regions using the PINN (22) as a function of the boundary conditions and the values ​​of the geometric parameters and to iteratively determine the velocity of the fluid in the regions based on the initial pressures. [8] Computer system (20) according to any one of claims 4 to 7, wherein the computer system (20) is configured to form a residual of the system of equations during the iterative determination of the velocities of the fluid and to evaluate the PINN (22) depending on the residual. [9] Method for simulating a flow (3) of a fluid in a volume (6) surrounding a component of a vehicle or technical system, the method comprising: - Determining initial velocities of the fluid in regions of the volume (6) using a physically informed neural network (PINN) (22) depending on boundary conditions for the flow (3) of the fluid at edges of the volume (6) and values ​​of geometric parameters, wherein a shape of the volume (6) is specified by the values ​​of the geometric parameters and the PINN (22) is trained on results of simulations of flows of the fluid; - Iterative determination of velocities of the fluid in the regions of the volume (6) depending on the boundary conditions and the initial velocities of the fluid in the regions, wherein the iteratively determined velocities describe the flow (3). [10] Computer program product comprising instructions executable by one or more processors, wherein execution of the instructions causes the processors to carry out the method according to claim 9.

Images