Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

In this paper we develop a new limiter for linear reconstruction on non-coordinatealigned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two-dimensional and linearity preserving. It separately limits the x and y components of the gradient, as opposed to a scalar limiter which limits all components simultaneously with one scalar. The limiter is based on solving a tiny linear program (LP) on each cell, using a very efficient version of the simplex method. A variety of computational results on triangular and embedded boundary meshes are presented. They demonstrate that the LP limiter successfully removes oscillations and significantly increases solution accuracy compared to a scalar limiter.