A semi-Lagrangian method on dynamically adapted octree meshes

Abstract

AbstractThe paper develops a semi-Lagrangian method for the numerical integration of the transport equation discretized on adaptive Cartesian cubic meshes. We use dynamically adaptive graded Cartesian grids. They allow for a fast grid reconstruction in the course of numerical integration. The suggested semi- Lagrangian method uses a higher order interpolation with a limiting strategy and a back-and-forth correction of the numerical solution. The interpolation operators have compact nodal stencils. In a series of experiments with dynamically adapted meshes, we demonstrate that the method has at least the second-order convergence and acceptable conservation and monotonicity properties.