An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation

TL;DR

This paper introduces an implicit Discontinuous Galerkin method with artificial compressibility for simulating incompressible two-phase flows, utilizing level set and adaptive mesh refinement techniques for improved interface capturing.

Contribution

It presents a novel implicit DG discretization combined with an artificial compressibility approach and AMR for efficient two-phase flow simulation.

Findings

Effective interface capturing demonstrated in benchmark tests

Adaptive mesh refinement improves resolution at fluid interfaces

Analysis of viscosity effects on flow behavior

Abstract

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L-stable TR-BDF2 method is adopted for the time discretization of the Navier-Stokes equations and of the level set method. Adaptive Mesh Refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out.