Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: Triangular elements
Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: Triangular elements
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DOI：
10.1016/j.jcp.2019.06.023
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
A. Mazaheri;Chi-Wang Shu;V. Perrier
中科院分区：
文献类型：
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作者：
A. Mazaheri;Chi-Wang Shu;V. Perrier
针对不规则单形单元上的二阶、三阶、四阶和五阶间断Galerkin（DG）格式，提出了两类新的紧致加权本质无振荡（韦诺）多项式限制器.所提出的WENO-DG程序是Zhu和Shu（2017）[25]，（2019）[26]的高阶韦诺有限体积和有限差分格式到高阶非结构DG格式的扩展。一个紧凑的正性保持限制器应用于解决方案，以确保压力和密度保持在物理范围内的所有时间。然后验证了有界WENO-DG在光滑区域保持了底层DG格式的形式精度。所提出的WENO-DG的性能也被证明与无粘测试用例，包括经典的黎曼问题，激波-湍流干扰，超燃冲压发动机，钝头体流动，和双马赫反射问题。
Two new classes of compact weighted essentially nonoscillatory (WENO) polynomial limiters are presented for second-, third-, fourth-, and fifth-order discontinuous Galerkin (DG) schemes on irregular simplex elements. The presented WENO-DG procedures are extensions of the high-order WENO finite-volume and finite-difference schemes of Zhu and Shu (2017) [25], (2019) [26] to high-order unstructured DG schemes. A compact positivity preserving limiter is applied to the solutions to ensure pressure and density remain within physical ranges at all time. It is then verified that the bounded WENO-DG maintains the formal order of accuracy of the underlying DG schemes in the smooth regions. The performance of the proposed WENO-DG is also demonstrated with inviscid test cases including the classical Riemann problems, shock-turbulence interaction, scramjet, blunt body flows, and the double Mach Reflection problems.