Computer simulation of physical fluids on a mesh in an arbitrary coordinate system

1. A computer implemented method for simulating a fluid flow about a surface of a solid, the method comprising:

receiving by the computing system, a coordinate system for representation of a curvilinear mesh that conforms to the surface of the solid;

simulating, with a lattice velocity set transport of particles in a volume of fluid, with the transport causing collision among the particles;

executing a distribution function for transport of the particles, with the distribution function including a particle collision determination and a change in particle distribution associated with the curvilinear mesh;

performing by the computing system, advection operations in the coordinate system under constraints applied to particle momentum values; and

mapping by the computer system values resulting from simulating onto the curvilinear mesh by translation of the particle momentum values and spatial coordinates determined in the coordinate system into momentum and spatial values in the curvilinear space.

2. The computer method of claim 1 wherein the solid surface is a curved, solid surface.

3. The computer method of claim 1 wherein the mesh is a curvilinear mesh in Euclidian space.

4. The computer method of claim 1 wherein the coordinate system is a non-Euclidian space defined in Riemannian geometry.

5. The computer method of claim 1 wherein the general curvilinear coordinate system has a one-to-one mapping to the selected coordinate system that is a Cartesian coordinate system in non-Euclidian space.

6. The computer method of claim 3 wherein particle advection is performed so that a particle distribution function is uniquely advected from one voxel (lattice site) to another voxel in each time step.

7. The computer method of claim 1 wherein the change in particle distribution causes the computing system to simulate an application of a force applied in each voxel at each time increment in the curvilinear mesh to enforce an exact momentum conservation in the coordinate system.

8. The computer method of claim 3 wherein volumetric representation is used so that each voxel in a general curvilinear mesh has a defined volume, and mass conservation is enforced and mass and momentum densities are defined.

9. The computer method of claim 1 wherein mapping further comprises:

determining momentum states constrained as a result of the representation of the mesh and the solid surface in the Cartesian coordinate system in non-Euclidean space.

10. Apparatus for simulating a fluid flow about a surface of a solid, the apparatus comprising:

a memory;

one or more processor devices configured to:

receive a coordinate system for representation of a curvilinear mesh that conforms to the surface of the solid;

simulate with a lattice velocity set, transport of particles in a volume of fluid, with the transport causing collision among the particles;

execute a distribution function for transport of the particles, with the distribution function including a particle collision determination and a change in particle distribution associated with the curvilinear mesh;

perform advection operations in the coordinate system under constraints applied to particle momentum values; and

map values resulting from simulating onto the curvilinear mesh by translation of the particle momentum values and spatial coordinates determined in the coordinate system into momentum and spatial values in the curvilinear space.

11. The apparatus of claim 10 wherein the solid surface is a curved, solid surface.

12. The apparatus of claim 10 wherein the mesh is a curvilinear mesh in Euclidian space.

13. The apparatus of claim 10 wherein the coordinate system is a non-Euclidian space defined in Riemannian geometry.

14. The apparatus of claim 10 wherein the general curvilinear coordinate system has a one-to-one mapping to the selected coordinate system that is a Cartesian coordinate system in non-Euclidian space.

15. The apparatus of claim 12 wherein particle advection is performed so that a particle distribution function is uniquely advected from one voxel to another voxel in each time step.

16. The apparatus of claim 10 wherein the change in particle distribution causes the computing system to simulate an application of a force applied in each voxel at each time increment in the curvilinear mesh to enforce an exact momentum conservation in the coordinate system.

17. The apparatus of claim 12 wherein volumetric representation is used so that each voxel in a general curvilinear mesh has a defined volume, and mass conservation is enforced and mass and momentum densities are defined.

18. The apparatus of claim 10 wherein mapping further comprises:

determining momentum states constrained as a result of the representation of the mesh and the solid surface in the Cartesian coordinate system in non-Euclidean space.

19. One or more machine-readable hardware storage devices storing instructions that are executable by one or more processing devices to cause a computer to

receive a coordinate system for representation of a curvilinear mesh that conforms to the surface of the solid;

simulate with a lattice velocity set, transport of particles in a volume of fluid, with the transport causing collision among the particles;

execute a distribution function for transport of the particles, with the distribution function including a particle collision determination and a change in particle distribution associated with the curvilinear mesh;

perform advection operations in the coordinate system under constraints applied to particle momentum values; and

map values resulting from simulating onto the curvilinear mesh by translation of the particle momentum values and spatial coordinates determined in the coordinate system into momentum and spatial values in the curvilinear space.

20. The one or more machine-readable hardware storage devices of claim 19 wherein the mesh is a curvilinear mesh in Euclidian space.