Central-moment discrete unified gas-kinetic scheme for incompressible two-phase flows with large density ratio

TL;DR

This paper introduces a novel central-moment discrete unified gas-kinetic scheme for simulating incompressible two-phase flows with large density ratios and high Reynolds numbers, demonstrating accurate results across various benchmarks.

Contribution

The paper develops a new DUGKS method using central moments and multiple relaxation times for improved multiphase flow simulation with large density ratios.

Findings

Accurately simulates flows with density ratios up to 1000.

Handles high Reynolds number flows up to 10^5.

Shows good agreement with reference and experimental data.

Abstract

In this paper, we proposed a central moment discrete unified gas-kinetic scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds number. Two sets of kinetic equations with central-moment-based multiple relaxation time collision operator are employed to approximate the incompressible Navier-Stokes equations and a conservative phase field equation for interface-capturing. In the framework of DUGKS, the first moment of the distribution function for the hydrodynamic equations is defined as velocity instead of momentum. Meanwhile, the zeroth moments of the distribution function and external force are also suitably defined such that a artificial pressure evolution equation can be recovered. Moreover, the Strang splitting technique for time integration is employed to avoid the calculation of spatial derivatives in the force term at cell faces. For the interface-capturing equation, two equivalent DUGKS methods that deal with the diffusion term differently using a source term as well as a modified equilibrium distribution function are presented. Several benchmark tests that cover a wide a range of density ratios (up to 1000) and Reynolds numbers (up to $10^5$) are subsequently carried out to demonstrate the capabilities of the proposed scheme. Numerical results are in good agreement with the reference and experimental data.