Pseudo-time stepping methods for space–time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

• Published in: Journal of computational physics Vol. 219; no. 2; pp. 622 - 643
• Main Authors: Klaij, C.M., van der Vegt, J.J.W., van der Ven, H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2006; Elsevier
• Subjects: Airfoils; Compressible Navier–Stokes equations; Computation; Computational techniques; Discontinuous Galerkin finite element methods; Discretization; Exact sciences and technology; Galerkin methods; Implicit–explicit Runge–Kutta methods; Mathematical analysis; Mathematical methods in physics; Navier-Stokes equations; Physics; Pseudo-time integration; Stability; Three dimensional; 02.70.Dh; Pseudo-time integration; Compressible Navier–Stokes equations; Implicit–explicit Runge–Kutta methods; 02.60.Cb; 03.40.Gc; Discontinuous Galerkin finite element methods; Reynolds number; Euler equations; Two dimensional flow; Calculation methods; Galerkin-Petrov method; Finite element method; Space-time; Discretization; Algebraic equation; Calculation; Runge-Kutta methods; Performance; Nonlinear systems; Navier-Stokes equations; Compressible Navier-Stokes equations; Implicit- explicit Runge-Kutta methods

The space–time discontinuous Galerkin discretization of the compressible Navier–Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge–Kutta methods developed for the Euler equations suffer from a severe s...