In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using 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.

在本文中，我们针对子曲线通量校正和凸限制满足双曲守恒律的高阶节点不连续Galerkin （DG）方法，该方法满足不变域的守恒性质。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健壮，低阶不变域保留方法进行混合。新的低阶离散化基于稀疏模板，且不会随多项式次数的增加而增加高阶DG方法 结果，当与高阶目标方法一起使用时，低阶方法的精度不会降低。该方法既适用于自然要强制执行离散最大原理的标量守恒定律，也适用于欧拉方程等守恒定律系统，对于这些定律必须执行密度的正性和特定熵的最小原理。在一些基准测试案例中给出了数值结果。