Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations

Highlights: • A positivity-preserving high order accurate finite volume hybrid HWENO scheme for compressible N-S equations. • The method is the high order accuracy and positivity-preserving. • The method is more efficient and more robust than the conventional HWENO methods. • The method is especially applicable for solving gas dynamics equations in low density and low pressure regime. In this paper, we construct a positivity-preserving high order accurate finite volume hybrid Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier-Stokes equations, by incorporating a nonlinear flux and a positivity-preserving limiter. HWENO schemes have more compact stencils than WENO schemes but with higher computational cost due to the auxiliary variables. The hybrid HWENO schemes use linear reconstructions in smooth region thus are more efficient than conventional HWENO schemes. However, the hybrid HWENO is not robust for many demanding problems. The positivity-preserving hybrid HWENO scheme in this paper is not only more efficient but also much more robust than the conventional HWENO method for both compressible Euler and compressible Navier-Stokes equations, especially for solving gas dynamics equations in low density and low pressure regime. Numerical tests on low density and low pressure problems are performed to demonstrate the robustness and the efficiency of the positivity-preserving hybrid HWENO scheme.