A bound-preserving and positivity-preserving finite volume WENO scheme for solving five-equation model of two-medium flows

In this paper, we develop a physical-constraint-preserving high-order finite volume WENO scheme for compressible two-medium gas-gas and gas-liquid interfacial flows. Using high-order WENO reconstruction and Lax-Friedrichs approximate Riemann flux, a high-order finite volume scheme for solving the five-equation transport model is presented by carefully designing the discretization of the non-conservative term. A novel and thorough analysis for deriving the sufficient condition to obtain physically admissible solutions, including bounded volume fractions, positive partial densities, internal energy and square of sound speed, is proposed and studied in details. Then, an effective bound- and positivity-preserving limiting procedure is developed based on the finite volume framework. Moreover, the proposed bound- and positivity-preserving limiting procedure is also applicable to a special type of hyperbolic tangent function as local solution profile, which is adopted to control numerical dissipation and sharpen material interfaces in this work. Typical problems of compressible gas-gas and gas-liquid two-medium flows are investigated to demonstrate the performance and capability of the proposed scheme. Numerical results demonstrate that the bound- and positivity-preserving limiting strategy is of vital importance in enhancing the robustness for high-order methods under severe flow conditions. (c) 2022 Elsevier B.V. All rights reserved.