Abstract 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.

中文翻译：

---

具有代数锐界面捕获的多材料流体动力学

摘要 提出了一种具有锐界面捕获的欧拉多材料流体动力学的有限体积方法。这里考虑了混合单元中具有有限速率压力松弛的压力-温度非平衡多材料系统。这种压力闭合有利于材料特性相关的压力松弛，而不是瞬时压力平衡，这反过来又允许使用未拆分的高阶时间积分器。用于界面捕获的修正双曲线切线 (THINC) 方法用于在三维非结构化网格上重建多材料 (> 2) 界面。提出了一种简单的修改，将 THINC 重建扩展到两种以上材料之间的界面。结果表明，改进的 THINC 可以捕获 2-4 个四面体单元内的多材料界面。由于 THINC 方法不需要几何重建，所提出的多材料方法算法简单，计算效率高。材料界面守恒量的一致重建确保在离散水平上满足守恒和闭合定律。通过在非结构化网格上解决的一系列测试问题，证明了所提出的方法是准确有效的多材料流体动力学计算的有希望的候选者。