A Bound-Preserving and Positivity-Preserving High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Compressible Multi-Medium Flows

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page B254-B279, June 2024.
Abstract. This work presents a novel bound-preserving and positivity-preserving direct arbitrary Lagrangian–Eulerian discontinuous Galerkin (ALE-DG) method for compressible multimedium flows by solving the five-equation transport model. The proposed method satisfies the discrete geometric conservation law (D-GCL) which indicates that uniform flow is precisely preserved during the simulation. More importantly, based on the D-GCL condition, we present a theoretical analysis on designing an efficient bound-preserving and positivity-preserving limiting strategy, which is able to maintain the boundedness of the volume fraction and the positivity of the partial density and internal energy, with the aim of avoiding the occurrence of inadmissible solutions and meanwhile improving the computational robustness. The accuracy and robustness of the proposed method are demonstrated by various one- and two-dimensional benchmark test cases. The numerical results verify the well capacity of the proposed high-order ALE-DG method for compressible multimedium flows with both the ideal and stiffened gas equation of state.