A new high-order sharp treatment of mixed cell solutions is introduced. The method is based on the reconstructed discontinuous Galerkin (rDG) scheme, in which we embed the known interfacial jump conditions as additional (physics-based) constraints in the least-squares reconstruction of the high-order degrees of freedom for multiple solution fields in the interfacial (mixed) cells. The approach allows us to avoid direct differentiation across multi-material interfaces, thus providing a robust and high-order accurate solution procedure. To track the interface dynamics, the method is combined with a hybrid of the level set (LS) and the front tracking (FT) methods — the so-called “Marker-Re-Distancing” (MRD) approach. As a fluid solver, we utilize the recently developed fully-implicit reconstructed discontinuous Galerkin method, developed for efficient and high-order resolution of all-speed compressible fluid dynamics. The new sharp physics-based reconstruction is incorporated into the overall Newton-Krylov-based solution procedure, with the residual of the mixed cell representing conservation of the mass, momentum and energy for the mixture. Thus, upon a convergence of the non-linear iterations, our treatment of interfacial cells is conservative.

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