An improved third‐order finite difference weighted essentially nonoscillatory scheme for hyperbolic conservation laws

2020 ◽  
Vol 92 (12) ◽  
pp. 1753-1777
Author(s):  
Guodong Li ◽  
Xiaogang Li ◽  
Pengfen Li ◽  
Dandan Cai
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Third Order ◽  
Hyperbolic Conservation ◽  
Weighted Essentially Nonoscillatory ◽  
Essentially Nonoscillatory

AN EFFICIENT THIRD-ORDER SCHEME FOR THREE-DIMENSIONAL HYPERBOLIC CONSERVATION LAWS

2012 ◽  
Vol 03 (04) ◽  
pp. 1250015
Author(s):  
LI CAI ◽  
JIAN-HU FENG ◽  
YU-FENG NIE ◽  
WEN-XIAN XIE
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Three Dimensional ◽  
Upwind Scheme ◽  
Third Order ◽  
Hyperbolic Conservation ◽  
Weighted Essentially Nonoscillatory ◽  
Order Scheme ◽  
Cweno Reconstruction ◽  
Three Space

In this paper, we present a third-order central weighted essentially nonoscillatory (CWENO) reconstruction for computations of hyperbolic conservation laws in three space dimensions. Simultaneously, as a Godunov-type central scheme, the CWENO-type central-upwind scheme, i.e., the semi-discrete central-upwind scheme based on our third-order CWENO reconstruction, is developed straightforwardly to solve 3D systems by the so-called componentwise and dimensional-by-dimensional technologies. The high resolution, the efficiency and the nonoscillatory property of the scheme can be verified by solving several numerical experiments.

scholarly journals Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
A. R. Appadu ◽  
A. A. I. Peer
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Temporal Integration ◽  
Weno Scheme ◽  
Integration Scheme ◽  
Advection Equation ◽  
Third Order ◽  
Hyperbolic Conservation ◽  
Weighted Essentially Nonoscillatory ◽  
Linear Advection Equation ◽  
Essentially Nonoscillatory

We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lowerL1errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.

WENO-TVD schemes for hyperbolic conservation laws

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Yousef Hashem Zahran
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Building Blocks ◽  
Second Order ◽  
Third Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Systematic Assessment ◽  
The Third ◽  
Seventh Order

The purpose of this paper is twofold. Firstly we carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [14] and [15].This modification is done by using two fluxes as building blocks in spatially fifth order WENO schemes instead of the second order TVD flux proposed by Titarev and Toro [14] and [15]. These fluxes are the second order TVD flux [19] and the third order TVD flux [20].Secondly, we propose to use these fluxes as a building block in spatially seventh order WENO schemes. The numerical solution is advanced in time by the third order TVD Runge–Kutta method. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws, in one and two dimension is presented. Systematic assessment of the proposed schemes shows substantial gains in accuracy and better resolution of discontinuities, particularly for problems involving long time evolution containing both smooth and non-smooth features.

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