High-resolution rotated grid method for conservation laws with embedded geometries

Abstract

We develop a second-order rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using an underlying Cartesian grid. Stability for time steps adequate for the regular part of the grid is obtained by increasing the domain of dependence of the numerical method near the embedded boundary by constructing h-boxes at grid cell interfaces. We describe a construction of h-boxes that not only guarantees stability but also leads to an accurate and conservative approximation of boundary cells that may be orders of magnitude smaller than regular grid cells. Of independent interest is the rotated difference scheme itself, on which the embedded boundary method is based.