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

TL;DR

This paper introduces a new implicit solver for the incompressible Navier-Stokes equations that combines DG spatial discretization with the TR-BDF2 time integration, demonstrating superior efficiency and robustness in complex simulations.

Contribution

The paper presents a novel implicit solver that integrates DG discretization with TR-BDF2, offering improved efficiency and accuracy over existing methods for incompressible flow simulations.

Findings

Demonstrates superior efficiency in benchmark tests

Enables accurate adaptive simulations in complex geometries

Suitable for large-scale industrial applications

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.