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

  • V´ıctor Llorente
  • Gonzalo Rubio
  • Antonio Pascau
  • Esteban Ferrer
  • M¨usl¨um Arıcı

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.

Keywords

one-dimensional transport equation, high-order methods,
Published
Jul 21, 2017
How to Cite
LLORENTE, V´ıctor et al. Comparison of the ENATE approach and discontinuous Galerkin spectral element method in 1D nonlinear transport equations. Computer Assisted Methods in Engineering and Science, [S.l.], v. 23, n. 2-3, p. 133–146, july 2017. ISSN 2299-3649. Available at: <http://cames.ippt.gov.pl/index.php/cames/article/view/168>. Date accessed: 18 oct. 2017.
Section
Articles