engleski

On efficiency and accuracy of WENO schemes

It is well known that the WENO schemes formally achieve high order of accuracy. On the other hand it was proven that in the presence of discontinuities the numerical methods are subject to a loss of formal accuracy. In this work we analyze the efficiency and accuracy of the numerical schemes on different one-dimensional problems. In order to make some quantitative comparison, we also perform computations for the first order Roe scheme. We evaluate the order of accuracy and convergence rates in the presence of discontinuities and present the distribution of numerical errors that occur through the numerical domain. The computational times for fixed resolution and simulation end time for the WENO and the first order scheme are measured and the relative cost is evaluated. Furthermore, we compute the numerical results for fixed amount of computational time up to the fixed time, with the considered high-order and first order schemes by using different grid resolution. The comparison of the obtained results is made and the grid convergence behavior of the considered schemes is presented. The detailed analysis and different measurements enable us to make some conclusions on the efficacy of the considered methods.

Weno; Roe; Accuracy; Discontinuities

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