Abstract: A physical process is simulated by storing in a memory state vectors for voxels. The state vectors include entries that correspond to particular momentum states of possible momentum states at a voxel. Interaction operations are performed on the state vectors. The interaction operations model interactions between elements of different momentum states. For a particular state vector, the interaction operations include calculating a desired distribution of elements for a voxel represented by the particular state vector, the desired distribution including a number of entries corresponding to the number of entries in the particular state vector.When one or more entries of the desired distribution has an out-of-range value, the desired distribution is modified to correct the out-of-range value. The state vector then is updated to correspond to the modified desired distribution. Finally, move operations are performed on the state vectors to reflect movement of elements to new voxels.

Abstract: A physical process is simulated by storing in a memory state vectors for voxels and a representation of at least one surface. The state vectors include entries that correspond to particular momentum states of set of possible momentum states at a voxel. Interaction operations are performed on the state vectors to model interactions between elements of different momentum states. In addition, surface interaction operations are performed on the representation of the surface. The surface interaction operations model interactions between the surface and elements of at least one voxel near the surface. The elements have a tangential momentum relative to the surface, and the surface interaction operations retain at least a portion of the tangential momentum of the elements. The portion of tangential momentum retained corresponds to a friction parameter. The friction parameter is varied based on changes in pressure near the surface.