We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.
Second order Implicit-Explicit Total Variation Diminishing schemes for the Euler system in the low Mach regime
University of Ferrara（费拉拉大学）；CNRS and Institut de Mathématiques de Bordeaux (IMB) Université de Bordeaux（法国国家科学研究中心与波尔多大学数学研究所）；Institut de Mathématiques de Toulouse (IMT), Université P. Sabatier（图卢兹大学数学研究所）
Consistency, convergence and error estimates for a mixed finite element / finite volume scheme to compressible Navier-Stokes equations with general inflow/outflow boundary data
A thermodynamically compatible semi-implicit finite volume scheme for the compressible Euler equations
University of Trento（特伦托大学）；Southern University of Science and Technology（南方科技大学）；La Sapienza Università di Roma（罗马第一大学）；Université de Strasbourg（斯特拉斯堡大学）；Inria
A Structure- and Pressure-Positivity-Preserving Semi-implicit IMEX Finite Volume Scheme for Ideal MHD at All Acoustic Mach and Alfvén Mach Numbers with Generic Equation of State
University of Cambridge（剑桥大学）；Université Savoie Mont Blanc（萨瓦勃朗西大学）；University of Ferrara（费拉拉大学）
Error estimates on a finite volume method for diffusion problems with interface on Eulerian grids
Xiangtan University（湘潭大学）；Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University（湘潭大学计算与工程科学模拟湖南省重点实验室）；Guangdong Provincial Engineering Technology Research Center for Data Science（广东省数据科学技术研究中心）；Institute of Fluid Physics, CAEP（中国工程物理研究院流体物理研究所）
