论文标题
不变域保存双曲系统的高阶光谱不连续近似
Invariant domain preserving high-order spectral discontinuous approximations of hyperbolic systems
论文作者
论文摘要
我们提出了一个有限的程序，以通过时间明确的离散高阶光谱不连续的近似解决方案来保护不变的域，以解决保护法的双曲线系统。如果该方案是离散保守的，并且在离散水平上满足几何保护定律，我们就会在时间步骤中得出一个条件，以确保细胞平均近似解决方案是不变域中状态的凸组合。然后使用这些状态定义局部边界，然后通过A后验缩放限制限制了细胞内的完整高阶近似解决方案。然后，用模态和淋巴结不连续的Galerkin方案进行数值实验证实了当前方法的稳健性和稳定性增强。
We propose a limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservation laws. Provided the scheme is discretely conservative and satisfy geometric conservation laws at the discrete level, we derive a condition on the time step to guaranty that the cell-averaged approximate solution is a convex combination of states in the invariant domain. These states are then used to define local bounds which are then imposed to the full high-order approximate solution within the cell via an a posteriori scaling limiter. Numerical experiments are then presented with modal and nodal discontinuous Galerkin schemes confirm the robustness and stability enhancement of the present approach.
