We present a new second order accurate structure-preserving finite volume scheme for the solution of the compressible barotropic two-phase model of Romenski et. al in multiple space dimensions. The governing equations fall into the wider class of symmetric hyperbolic and thermodynamically compatible (SHTC) systems and consist of a set of first-order hyperbolic partial differential equations (PDE). In the absence of algebraic source terms, the model is subject to a curl-free constraint for the relative velocity between the two phases. The main objective of this paper is, therefore, to preserve this structural property exactly also at the discrete level. The new numerical method is based on a staggered grid arrangement where the relative velocity field is stored in the cell vertexes while all the remaining variables are stored in the cell centers. This allows the definition of discretely compatible gradient and curl operators, which ensure that the discrete curl errors of the relative velocity field remain zero up to machine precision. A set of numerical results confirms this property also experimentally.

翻译：本文提出了一种新的二阶精度结构保持有限体积格式，用于求解多空间维度下Romenski等人建立的可压缩气压两相流模型。控制方程属于对称双曲热力学相容（SHTC）系统大类，包含一组一阶双曲型偏微分方程（PDE）。在无代数源项时，模型要求两相相对速度场满足无旋约束。本文主要目标是在离散层面精确保持该结构特性。新数值方法基于交错网格布局，其中相对速度场存储在单元顶点，而其余变量存储在单元中心。这种设计可定义离散兼容的梯度算子和旋度算子，确保相对速度场的离散旋度误差在机器精度范围内保持为零。一系列数值结果在实验层面验证了该特性。