 High order semi-implicit weighted compact nonlinear scheme for viscous Burgers’ equationsYanqun Jiang, Xun Chen, Rong Fan and Xu Zhang Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 607-621 Abstract: This paper develops a high order semi-implicit weighted compact nonlinear scheme (WCNS) for one- and two-dimensional viscous Burgers’ equations. This semi-implicit WCNS combines a fifth-order WCNS with a third-order implicit-explicit Runge–Kutta (IMEX-RK) time-stepping method. The advection terms of viscous Burgers’ equations are treated explicitly, while the viscosity terms are treated implicitly. Stability analysis shows that the CFL condition of the semi-implicit WCNS is controlled only by the advection terms. Compared to the explicit time-stepping method, the semi-implicit method has the advantage in terms of computational efficiency. Numerical results validate the accuracy and efficiency of the semi-implicit WCNS. This method can also solve viscous Burgers’ equations with large Reynolds numbers and has high-resolution shock-capturing ability. Keywords: Semi-implicit; Weighted compact nonlinear scheme; High-resolution; Viscous Burgers’ equations; Shock-capturing ability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:607-621 DOI: 10.1016/j.matcom.2021.06.006 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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