DoD Stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension

作者：

Highlights：

• Presentation of Domain of Dependence (DoD) stabilization for DG schemes.

• Penalty stabilization for enabling explicit time stepping on cut cell meshes.

• Extension of DoD stabilization to non-linear systems and higher order polynomials.

• Theoretical results include proofs of monotonicity and L2 stability.

• Numerical results confirm high-order accuracy and robustness.

摘要

•Presentation of Domain of Dependence (DoD) stabilization for DG schemes.•Penalty stabilization for enabling explicit time stepping on cut cell meshes.•Extension of DoD stabilization to non-linear systems and higher order polynomials.•Theoretical results include proofs of monotonicity and L2 stability.•Numerical results confirm high-order accuracy and robustness.

论文关键词：Embedded boundary method,Cut cell,Small cell problem,Discontinuous Galerkin method,DoD Stabilization,Hyperbolic conservation law

论文评审过程：Received 28 June 2021, Revised 25 October 2021, Accepted 2 December 2021, Available online 27 December 2021, Version of Record 27 December 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126854