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

• Published in: International journal for numerical methods in fluids 2022-09, Vol.94 (9), p.1484-1516
• Main Authors: Orlando, Giuseppe, Della Rocca, Alessandro, Barbante, Paolo Francesco, Bonaventura, Luca, Parolini, Nicola
• Format: Article
• Language: English
• Subjects: Benchmarks; discontinuous Galerkin methods; Discretization; ESDIRK methods; Fluid flow; implicit methods; incompressible flows; Industrial applications; Mathematical analysis; mesh adaptation; Methods; Navier-Stokes equations; Solvers
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.5098

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. We propose an accurate and robust solver for the incompressible Navier–Stokes equations. The method is based on a DG spatial discretization and on the TR‐BDF2 method for time discretization and its superior efficiency with respect to other widely used implicit approaches has been shown in a number of classical benchmarks. Good scaling properties of the parallel implementation in the framework of the deal.II software package, as well as accurate simulations in complex geometries, are presented, making the proposed solver attractive also for large scale industrial applications.