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Open AccessArticle

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

1
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(10), 211; https://doi.org/10.3390/math6100211
Received: 27 September 2018 / Revised: 11 October 2018 / Accepted: 14 October 2018 / Published: 18 October 2018
(This article belongs to the Special Issue Numerical Methods for Partial Differential Equations)
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. View Full-Text
Keywords: Lax–Wendroff-type time discretization; WENO schemes; finite volume method; nonlinear Euler system; high order accuracy Lax–Wendroff-type time discretization; WENO schemes; finite volume method; nonlinear Euler system; high order accuracy
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Dong, H.; Lu, C.; Yang, H. The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations. Mathematics 2018, 6, 211.

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