Open AccessOptimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws
Author(s) -
Appanah Rao Appadu,
Arshad Ahmud Iqbal Peer
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/428681
Subject(s) - conservation law , dissipative system , discretization , advection , dissipation , mathematics , algorithm , convergence (economics) , hyperbolic partial differential equation , dispersion (optics) , order (exchange) , computer science , mathematical analysis , partial differential equation , physics , thermodynamics , optics , economics , economic growth , finance
We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO)scheme is derived by coupling a WENO spatial discretization scheme with a temporal integrationscheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipativeproperties when used to approximate the 1D linear advection equation and use a technique ofoptimisation to find the optimal cfl number of the scheme. We carry out some numerical experimentsdealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at somedifferent cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation,and lower L1 errors. Lastly, we test numerically the order of convergence of the WENO3 scheme
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