Multi-material hydrodynamics with algebraic sharp interface capturing

•A finite volume method for multi-material (more than 2 materials) hydrodynamics with sharp interface capturing is presented for unstructured meshes.•The non-equilibrium multi-material system with finite-rate material property dependent pressure relaxation in mixed-cells is considered here, which allows use of unsplit high-order time-integrators.•A novel modification for the tangent of hyperbola for interface capturing (THINC) method is proposed, which allows algebraic interface reconstruction for more than two materials. The proposed method can capture multimaterial interfaces within 2–4 tetrahedral cells.•Since no geometric reconstructions are required by the THINC method, it is algorithmically simple, and computationally efficient. A finite volume method for Eulerian multi-material hydrodynamics with sharp interface capturing is presented. The pressure-temperature non-equilibrium multi-material system with finite-rate pressure relaxation in mixed-cells is considered here. This pressure closure facilitates material-property-dependent pressure relaxation, rather than instantaneous pressure equilibration, which in turn allows the use of unsplit high-order time-integrators. A modified tangent of hyperbola for interface capturing (THINC) method is used to reconstruct multi-material (>2) interfaces, on three-dimensional unstructured meshes. A simple modification which extends the THINC reconstruction to interfaces between more than two materials is proposed. It is demonstrated that the modified THINC can capture multi-material interfaces within 2–4 tetrahedral cells. Since no geometric reconstructions are required by the THINC method, the presented multi-material method is algorithmically simple, and computationally efficient. Consistent reconstructions of conserved quantities at material interfaces ensure that conservation and closure laws are satisfied at the discrete level. Through a suite of test problems solved on unstructured meshes, it is demonstrated that the presented method is a promising candidate for accurate and efficient multi-material hydrodynamics computations.