Abstract
A recently developed high-order implicit shock tracking method is novelly applied to a benchmark problem in two-dimensional compressible reactive flow, and results of remarkably high accuracy are achieved relative to competing shock capturing schemes. High-order implicit shock tracking is a discontinuous Galerkin discretization of conservation laws that simultaneously computes an approximate flow solution and aligns faces of the computational mesh with discontinuities in the flow to provide nonlinear stabilization and an improved approximation to the solution. The model problem is chosen such that its exact solution is available in analytic form to facilitate a detailed study of the truncation error of the tracking method relative to a nominally fifth-order weighted essentially nonoscillatory method. We show the implicit tracking method is able to robustly align the mesh with the shock and, particularly for polynomial bases of degree greater than 1, provide a high-quality approximation to the exact solution on meshes far coarser than required by standard methods. Finally, we demonstrate the tracking method obtains near optimal convergence rates in several error metrics for the problem under consideration.
Accepted Version
Published Version
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