Fast time implicit-explicit discontinuous Galerkin method for convection dominated flow problems

An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving unsteady second-order partial differential equations. The time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term. The implicit procedure uses a fast iterative algorithm with reduced evaluation cost introduced in [Renac, Marmignon, and Coquel, SIAM J. Sci. Comput., 34, A370– A394, 2012]. The method is here extended to convection dominated flow problems. A second-order discretization in time is achieved by decomposing the integrations of convective and diffusive terms with a splitting method. Numerical examples are presented for the linear convection-diffusion equation in one and two space dimensions. The performance of the present method is seen to be improved in terms of CPU time when compared to a full implicit discretization of the parabolic terms in a wide range of Peclet numbers.

Keywords

discontinuous Galerkin method, linear convection-diffusion equation, convection dominated problems, implicit-explicit time discretization, splitting method

2010 Mathematics Subject Classification

65N12, 65N30

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Published 23 July 2012