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Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. (English) Zbl 1102.76035

Summary: The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a nonlinear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge-Kutta methods developed for Euler equations suffer from a severe stability constraint linked to the viscous part of the equations, and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare our method with an implicit-explicit Runge-Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a two-dimensional airfoil and a three-dimensional delta wing at low and moderate Reynolds numbers.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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