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. The state vectors include entries that correspond to particular momentum states of possible momentum states at a voxel. Iinteraction 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 performing energy-exchanging interaction operations that model interactions between elements of different momentum states that represent different energy levels. A rate factor for the voxel represented by the particular state vector affects a degree to which energy-exchanging interaction operations cause a transfer of elements from states representing lower energy levels to states representing higher energy levels, rather than from states representing higher energy levels to states representing lower energy levels.

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.

Abstract: To simulate physical processes, state vectors for each of multiple voxels are stored in a memory along with a representation for each of multiple facets that are sized and oriented independently of the size and orientation of the voxels and, in combination, represent one or more surfaces. Each state vector includes multiple entries, each of which corresponds to a number of elements at a particular momentum state of multiple possible momentum states at a voxel. Interaction operations that model interactions between elements of different momentum states are performed on the state vectors, and surface interaction operations that model interactions between a facet and elements at one or more voxels near the facet are performed on the representations of facets. Finally, move operations that reflect movement of elements to new voxels are performed on the state vectors.

Abstract: A computer implemented method for simulating a physical process. The method includes storing in a memory a state vector for each of a number of voxels. Each state vector includes a plurality of integers, each of which corresponds to a particular momentum state of a number of possible momentum states at a voxel and represents the number of elements having the particular momentum state. Each integer has more than two possible values. The method also includes performing interaction operations that model interactions between elements of different momentum states and include interaction rules that operate on a subset of the integers of a state vector. The interaction rules comprise a collision operator that transfers between integers representing a first set of momentum states and integers representing a second set of momentum states a number of elements that is determined based on the number of elements in the first and second sets of momentum states.

Abstract: A computer implemented method for simulating a physical process. The method includes storing in a memory a state vector for each of a number of voxels. Each state vector includes a plurality of integers, each of which corresponds to a particular momentum state of a number of possible momentum states at a voxel and represents the number of elements having the particular momentum state. Each integer has more than two possible values. The method also includes performing interaction operations on the state vectors that model interactions between elements of different momentum states, performing viscosity modification operations on the state vectors to change the viscosity of the simulated physical process, and performing move operations on the state vectors that reflect movement of elements to new voxels.

Abstract: A computer implemented method for simulating a physical process. The method includes storing in a memory a state vector for each of a number of voxels (i.e., lattice sites). Each state vector includes a plurality of integers, each of which corresponds to a particular momentum state of a number of possible momentum states at a voxel (lattice site) and represents the number of elements having the particular momentum state. Each integer has more than two possible values. The method also includes performing interaction operations on the state vectors that model interactions between elements of different momentum states and performing move operations on the state vectors that reflect movement of elements to new voxels.