In this paper, a simple fifth-order finite difference Hermite WENO (HWENO) scheme combined with limiter is proposed for one- and two- dimensional hyperbolic conservation laws. The fluxes in the governing equation are approximated by the nonlinear HWENO reconstruction which is the combination of a quintic polynomial with two quadratic polynomials, where the linear weights can be artificial positive numbers only if the sum equals one. And other fluxes in the derivative equations are approximated by high-degree polynomials directly. For the purpose of controlling spurious oscillations, an HWENO limiter is applied to modify the derivatives. Instead of using the modified derivatives both in fluxes reconstruction and time discretization as in the modified HWENO scheme (J. Sci. Comput., 85:29, 2020), we only apply the modified derivatives in time discretization while remaining the original derivatives in fluxes reconstruction. Comparing with the modified HWENO scheme, the proposed HWENO scheme is simpler, more accurate, efficient and higher resolution. In addition, the HWENO scheme has a more compact spatial reconstructed stencil and greater efficiency than the classical fifth-order finite difference WENO scheme of Jiang and Shu. Various benchmark numerical examples are presented to show the fifth-order accuracy, great efficiency, high resolution and robustness of the proposed HWENO scheme.
翻译:在本文件中,为一维和二维双曲线保护法提出了简单第五级限值差异Hermite WENO(HWINO)和限值组合的一维和二维双维双曲线保护法。管理方程式的通量近似于非线性HWENO重建,这是将五进制多元数与两个四进制多元数相结合的组合,线性加权数只有在总和等于一的情况下才能为人为正数。衍生方程式的其他通量则直接由高度多元复合方程相近。为了控制虚假的振动,将HWENO限制用于修改衍生物。在调整流动的HWENO办法(J. Sci. Comput. 85:29, 2020)的重组和时间分解中,我们只将修改后的衍生物在时间分解中应用,同时保留通度重建的原始衍生物。拟议的HWENO方案与经修改的HWENO计划相近、更准确、更高效和更高分辨率的HWENO限制。此外,HWENO高分辨率和高清晰度计划也比HWE-HWE-S-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-S-G-S-S-S-S-S-S-S-S-S-S-S-S-G-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-