Abstract

A combined scheme for the discontinuous Galerkin (DG) method is proposed. This scheme monotonically localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the computed weak solutions. In this scheme, a nonmonotone version of the third-order DG method is used as a baseline scheme and a monotone version of this method is used as an internal scheme, in which a nonlinear correction of numerical fluxes is used. Tests demonstrate the advantages of the new scheme as compared to standard monotonized variants of the DG method.

中文翻译：

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组合DG方案可在冲击波区域保持更高的精度

摘要

提出了一种不连续Galerkin（DG）方法的组合方案。该方案单调地定位了冲击波的前沿，同时在所计算的弱解的平滑度区域中保持了提高的准确性。在此方案中，将三阶DG方法的非单调版本用作基线方案，并将此方法的单调版本用作内部方案，其中使用了数值通量的非线性校正。测试证明了与DG方法的标准单调变体相比，新方案的优势。