论文标题
稀疏不变域保存不连续的盖尔金方法，并具有子电池凸限
Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
论文作者
论文摘要
在本文中，我们开发了高阶淋巴结不连续的Galerkin（DG）方法，用于使用子细胞通量校正和凸限制来满足不变结构域的性能。这些方法基于子电池通量校正传输（FCT）方法，该方法涉及将高阶目标方案与使用图粘度技术获得的强大，低阶不变域保存方法相结合。新的低阶离散化是基于稀疏模板，这些模板不会随着高阶DG方法的多项式程度而增加。结果，与高阶目标方法一起使用时，低阶方法的精度不会降低。该方法适用于两种标量保护定律，该法律自然执行了离散的最大原则，以及诸如Euler方程的保护制度，其密度的阳性和对特定熵的最低原则的阳性。数值结果在许多基准测试案例上显示。
In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using a subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. The new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.
