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1 Computer Assisted Methods in Engineering and Science

1 2016

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Comparison of the ENATE approach and discontinuous Galerkin spectral element method in 1D nonlinear transport equations

Llorente V., Rubio G., Pascau A., Ferrer E., Arıcı M.

Computer Assisted Methods in Engineering and Science

2016

Vol. 23, no. 2/3

133--146

In this paper a comparison of the performance of two ways of discretizing the nonlinear convection-diffusion equation in a one-dimensional (1D) domain is performed. The two approaches can be considered within the class of high-order methods. The first one is the discontinuous Galerkin method, which has been profusely used to solve general transport equations, either coupled as the Navier-Stokes equations, or on their own. On the other hand, the ENATE procedure (Enhanced Numerical Approximation of a Transport Equation), uses the exact solution to obtain an exact algebraic equation with integral coefficients that link nodal values with a three-point stencil. This paper is the first of a thorough assessment of ENATE by comparing it with well established high-order methods. Several test cases of the steady Burgers’ equation with and without source have been chosen for comparison.