A low-dissipation numerical method based on boundary variation diminishing principle for compressible gas-liquid two-phase flows with phase change on unstructured grid

TL;DR

This paper introduces a low-dissipation numerical scheme for simulating compressible gas-liquid flows with phase change on unstructured grids, effectively capturing interfaces and discontinuities with high accuracy.

Contribution

It develops a novel MUSCL-THINC/QQ-BVD scheme that adaptively combines methods for smooth and discontinuous solutions based on the BVD principle, improving interface capturing accuracy.

Findings

Successfully captures contact discontinuities with low dissipation.

Resolves dynamically generated gas-liquid interfaces clearly.

Demonstrates high accuracy on benchmark tests.

Abstract

A low-dissipation numerical method for compressible gas-liquid two-phase flow with phase change on unstructured grids is proposed. The governing equations adopt the six-equation model. The non-conservative terms included in the volume fraction and total energy equations of the six-equation model are defined on cell boundaries using second-order accurate approximations and calculated without interpolating the spatial derivatives. To capture discontinuities such as contact discontinuities and gas-liquid interfaces with low dissipation, the MUSCL-THINC/QQ-BVD scheme, which combines the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) method and the Tangent Hyperbola for INterface Capturing method with Quadratic surface representation and Gaussian Quadrature (THINC/QQ) method, is employed. The MUSCL method is one of the mainstream numerical solvers for compressible flows, achieving second-order accuracy for smooth solutions, but it introduces excessive numerical dissipation errors near discontinuous solutions. The THINC/QQ method uses a reconstruction function developed for interface capturing on unstructured grids, making use of a sigmoidal function with a quadratic surface. By combining these reconstruction functions according to the Boundary Variation Diminishing (BVD) principle, the MUSCL method is selected for smooth solutions, while the THINC/QQ method is chosen for discontinuous solutions, preserving the solution structure accurately. Several benchmark tests are solved, demonstrating that the MUSCL-THINC/QQ-BVD scheme not only captures contact discontinuities with low dissipation but also resolves dynamically generated gas-liquid interfaces due to phase changes clearly.