Lattice Boltzmann equation hydrodynamics

By inserting position and time dependent “source” or “forcing” terms into the microscopic evolution equation of a lattice Boltzmann fluid and treating the generalized scheme within the usual Chapman-Enskog methodology, we show that the emergent dynamics of the lattice fluid may be usefully transformed. Our method of adjustment is demonstrated by implementing the cylindrical polar coordinate form of the continuity and momentum equations on a rectangular lattice and generating results for pipe flow. With straightforward systematic adjustment of the simulation, our approach produces results in excellent agreement with theory.