RCM‐TVD hybrid scheme for hyperbolic conservation laws |
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| Authors: | Yousef Hashem Zahran |
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| Institution: | Physics and Mathematics Department, Faculty of Engineering, Port Said, Egypt |
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| Abstract: | We describe a hybrid method for the solution of hyperbolic conservation laws. A third‐order total variation diminishing (TVD) finite difference scheme is conjugated with a random choice method (RCM) in a grid‐based adaptive way. An efficient multi‐resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with RCM while the smooth regions are computed with the more efficient TVD scheme. The hybrid scheme captures correctly the discontinuities of the solution and saves CPU time. Numerical experiments with one‐ and two‐dimensional problems are presented. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | random choice method Runge– Kutta methods TVD schemes conservation laws Euler equations finite difference scheme multi‐resolution Burger equation |
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