In (Dzanic, J. Comp. Phys., 508:113010, 2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

翻译：在 (Dzanic, J. Comp. Phys., 508:113010, 2024) 中，提出了一种针对高阶间断伽辽金格式的限制方法，该方法能够在解上连续施加约束（即，在单元内处处满足）。虽然该方法对线性约束泛函是精确的，但对于非线性约束泛函，它仅施加了充分（而非最小必要）的限制量。本文简要展示了如何通过非线性限制过程将这一限制方法扩展至一般非线性拟凹约束泛函的精确实现，从而减少不必要的数值耗散。以可压缩气体动力学方程中的非线性压力和熵约束为例，分别采用了解析方法和迭代方法进行实现。