Interpolation Methods and the Accuracy of Lattice-Boltzmann Mesh Refinement

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adaptively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite-volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examples highlighting the mesh adaptivity of this method are also provided.