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.

在本文中，我们通过结合非线性通量和正性保留限制器，为可压缩 Navier-Stokes 方程构建了一种保留正性的高阶精确有限体积混合 Hermite 加权基本非振荡 (HWENO) 方案。HWENO 方案比 WENO 方案具有更紧凑的模板，但由于辅助变量而具有更高的计算成本。混合 HWENO 方案在平滑区域使用线性重建，因此比传统的 HWENO 方案更有效。然而，混合 HWENO 对于许多苛刻的问题并不稳健。对于可压缩欧拉方程和可压缩 Navier-Stokes 方程，本文中的正性保留混合 HWENO 方案不仅更有效，而且比传统的 HWENO 方法更稳健，特别适用于求解低密度和低压状态下的气体动力学方程。对低密度和低压问题进行了数值测试，以证明保留正性的混合 HWENO 方案的稳健性和效率。