Discrete unified gas kinetic scheme with force term for incompressible fluid flows

TL;DR

This paper develops a modified discrete unified gas kinetic scheme with force terms for more accurate simulation of incompressible fluid flows, incorporating pressure boundary conditions and demonstrating effectiveness through various numerical tests.

Contribution

A novel DUGKS model with force term and pressure boundary scheme is proposed, reducing compressible effects and improving simulation accuracy for incompressible flows.

Findings

Reduces compressible effects in DUGKS for incompressible flows

Achieves second-order accuracy with NEQ boundary scheme

Successfully simulates 3D lid-driven flow with good agreement to benchmarks

Abstract

The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme with discretization of particle velocity space, which combines the advantages of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme (UGKS) method, such as the simplified flux evaluation scheme, flexible mesh adaption and the asymptotic preserving properties. However, DUGKS is proposed for near incompressible fluid flows, the existing compressible effect may cause some serious errors in simulating incompressible problems. To diminish the compressible effect, in this paper a novel DUGKS model with external force is developed for incompressible fluid flows by modifying the approximation of Maxwellian distribution. Meanwhile, due to the pressure boundary scheme, which is wildly used in many applications, has not been constructed for DUGKS, the non-equilibrium extrapolation (NEQ) scheme for both velocity and pressure boundary conditions is introduced. To illustrate the potential of the proposed model, numerical simulations of steady and unsteady flows are performed. The results indicate that the proposed model can reduce the compressible effect efficiently against the original DUGKS model, and the NEQ scheme fits well with our model as they are both of second-order accuracy. We also implement the proposed model in simulating the three dimensional problem: cubical lid-driven flow. The comparisons of numerical solutions and benchmarks are presented in terms of data and topology. And the motion pattern of the fluid particles in a specific area is characterized for the steady-state cubical lid-driven flows.