2012 journal article

An implicit discontinuous Galerkin method for the unsteady compressible Navier-Stokes equations

COMPUTERS & FLUIDS, 53, 133–144.

By: H. Luo n, H. Segawa n & M. Visbal*

co-author countries: United States of America 🇺🇸
author keywords: Discontinuous Galerkin methods; Implicit methods; Compressible Navier-Stokes equations
Source: Web Of Science
Added: August 6, 2018

A high-order implicit discontinuous Galerkin method is developed for the time-accurate solutions to the compressible Navier–Stokes equations. The spatial discretization is carried out using a high order discontinuous Galerkin method, where polynomial solutions are represented using a Taylor basis. A second order implicit method is applied for temporal discretization to the resulting ordinary differential equations. The resulting non-linear system of equations is solved at each time step using a pseudo-time marching approach. A newly developed fast, p-multigrid is then used to obtain the steady state solution to the pseudo-time system. The developed method is applied to compute a variety of unsteady subsonic viscous flow problems. The numerical results obtained indicate that the use of this implicit method leads to significant improvements in performance over its explicit counterpart, while without significant increase in memory requirements.