The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Haoyu Dong, Changna Lu and Hongwei Yang
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Haoyu Dong: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Changna Lu: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Hongwei Yang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2018, vol. 6, issue 10, 1-17

Abstract: We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

Keywords: Lax–Wendroff-type time discretization; WENO schemes; finite volume method; nonlinear Euler system; high order accuracy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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