论文标题
五阶有限差异HWENO方案与双曲线保护法的限制器结合
A fifth-order finite difference HWENO scheme combined with limiter for hyperbolic conservation laws
论文作者
论文摘要
在本文中，提出了一个简单的五阶有限差源自WENO（HWENO）方案与限制器相结合的一维和二维双曲线保护法。管理方程式中的通量通过非线性Hweno重建近似，该重建是五级多项式与两个二次多项式的组合，其中只有当总和等于一个时，线性重量才能是人为的正数。导数方程中的其他通量直接通过高度多项式近似。为了控制虚假的振荡，使用Hweno限制器来修改衍生物。我们仅在修改后的HWENO方案（J.Sci。Comput。，85：29，2020）中使用修改后的衍生物和时间离散化，而是在时间离散的同时将原始的衍生物应用于磁通量。与修改的Hweno方案相比，提出的HWENO方案更简单，更准确，有效且更高分辨率。此外，与经典的第五阶有限差异差异WENO方案相比，HWENO方案具有更紧凑的空间重建模板和更高的效率。提出了各种基准数值示例，以显示拟议的Hweno方案的五阶准确性，高效率，高分辨率和鲁棒性。
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.
