Communications in Mathematical Sciences

Volume 10 (2012)

Number 4

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

Pages: 1161 – 1172



Frédéric Coquel (CNRS and CMAP, Ecole Polytechnique, Palaiseau, France)

Claude Marmignon (ONERA, French Aerospace Lab, Châtillon, France)

Florent Renac (ONERA, French Aerospace Lab, Châtillon, France)


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.


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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