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

Víctor Llorente; Gonzalo Rubio; Antonio Pascau; Esteban Ferrer; Müslüm Arıcı

doi:10.24423/cames.168

Víctor Llorente Fluid Mechanics Group and LIFTEC, University of Zaragoza and CSIC, Zaragoza
Gonzalo Rubio Applied Mathematics and Statistics Department, Polytechnical University of Madrid, Madrid
Antonio Pascau Fluid Mechanics Group and LIFTEC, University of Zaragoza and CSIC, Zaragoza
Esteban Ferrer Applied Mathematics and Statistics Department, Polytechnical University of Madrid, Madrid
Müslüm Arıcı Mechanical Engineering Department, Kocaeli University, Kocaeli, Turkey/Fluid Mechanics Group and LIFTEC, University of Zaragoza, Zaragoza

DOI: http://dx.doi.org/10.24423/cames.168

Abstract

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 thorough assessments 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.

*The paper was presented during the Eurotherm Seminar No 109 – Numerical Heat Transfer 2015.

Keywords

one-dimensional transport equation, high-order methods,

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