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A Hybrid WENO Scheme for Conservation Laws

We describe a hybrid method for the solution of hyperbolic conservation laws. A fourth-order total variation diminishing (TVD) finite difference scheme is conjugated with the seven-order WENO scheme. An efficient multi-resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with the seven-order WENO scheme 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 oneand two-dimensional problems are presented.