Robust 3D multi‐material hydrodynamics using discontinuous Galerkin methods

Abstract

A high‐order discontinuous Galerkin (DG) method is presented for nonequilibrium multi‐material () flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high‐order accurate solutions in smooth single‐material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high‐order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three‐dimensional multi‐material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi‐material solutions can be obtained by the DG method, as compared to second‐order finite volume methods.