Comparison of the ENATE approach and discontinuous Galerkin spectral element method in 1D nonlinear transport equations
Computer Assisted Methods in Engineering and Science, cilt.23, sa.2-3, ss.133-146, 2016 (Scopus)
- Yayın Türü: Makale / Özet
- Cilt numarası: 23 Sayı: 2-3
- Basım Tarihi: 2016
- Dergi Adı: Computer Assisted Methods in Engineering and Science
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.133-146
- Anahtar Kelimeler: High-order methods, One-dimensional transport equation
- Kocaeli Üniversitesi Adresli: Evet
Özet
Copyright 2016 by Institute of Fundamental Technological Research, Polish Academy of SciencesIn 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 benn 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.