An Adaptive Mesh Refinement Strategy with Conservative Space-Time Coupling for the Lattice-Boltzmann Method

A conservative lattice-Boltzmann method is presented for solving the time-dependent Navier-Stokes equations at low Mach numbers on lattices that are adaptively refined in space and time. A method for coupling the interfaces between grids at different resolutions was constructed following techniques established for finite-volume computational fluid dynamics methods. The effectiveness of the new coupling method, which relies on a spacetime interpolation and solving constrained least-squares problems to ensure conservation is compared against similar approaches relying only on spatial interpolation.