An efficient and accurate implicit DG solver for the incompressible Navier-Stokes equations

Abstract

We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely used implicit approaches. The parallel implementation of the proposed method in the framework of the deal.II software package allows for accurate and efficient adaptive simulations in complex geometries, which makes the proposed solver attractive for large scale industrial applications.

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• An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation
• On the evolution equations of interfacial variables in two-phase flows