An adaptive fully discontinuous Galerkin level set method for incompressible multiphase flows

• Published in: International journal of numerical methods for heat & fluid flow 2018-08, Vol.28 (6), p.1256-1278
• Main Authors: Karakus, Ali, Warburton, Tim, Aksel, Mehmet Haluk, Sert, Cuneyt
• Format: Article
• Language: English
• Subjects: Accuracy; Adaptation; Adaptive systems; Computational fluid dynamics; Computer memory; Computer simulation; Conjugate gradient method; Conservation; Dam failure; Dam stability; Discretization; Efficiency; Flow equations; Fluid flow; Fluids; Galerkin method; Incompressible flow; Instability; Interfaces; Methods; Model accuracy; Modelling; Multiphase flow; Navier-Stokes equations; Numerical analysis; Ratios; Simulation; Taylor instability; Topology; Unstructured grids (mathematics); Viscosity
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-03-2017-0098

Purpose This study aims to focus on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation. Design/methodology/approach Nodal discontinuous Galerkin discretization is used for incompressible Navier–Stokes, level set advection and reinitialization equations on adaptive unstructured elements. Implicit systems arising from the semi-explicit time discretization of the flow equations are solved with a p-multigrid preconditioned conjugate gradient method, which minimizes the memory requirements and increases overall run-time performance. Computations are localized mostly near the interface location to reduce computational cost without sacrificing the accuracy. Findings The proposed method allows to capture interface topology accurately in simulating wide range of flow regimes with high density/viscosity ratios and offers good mass conservation even in relatively coarse grids, while keeping the simplicity of the level set interface modeling. Efficiency, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases of sloshing, dam break and Rayleigh–Taylor instability. Originality/value A fully discontinuous Galerkin, high-order, adaptive method on unstructured grids is introduced where flow and interface equations are solved in discontinuous space.