Homotopy Continuation for Correction Procedure via Reconstruction - Discontinuous Galerkin (CPR-DG) Methods

Abstract

Homotopy continuation for correction procedure via reconstruction -discontinuous Galerkin (CPR-DG) methods is developed for solving steady state hyperbolic conservation laws. The efficacy of homotopy continuation has been demonstrated using both 1D and 2D steady flow problems. According to the test results, it is found that homotopy continuation can work robustly on flow simulations of shock capturing for a wide range of grid sizes and polynomial orders without parameter tuning.