A. I. Delis and I. K. Nikolos A novel multidimensional solution reconstruction and edge-based limiting procedure for unstructured cell-centered finite volumes with application to shallow water dynamics International Journal for Numerical Methods in Fluids 71
A novel geometrical approach for linear reconstruction and limiting of the numerical solution on cell-centered finite volume methods, which is independent of the (approximate) Riemann solver used, is presented. Within the proposed reconstruction, edge-based limiters can be applied in a multi-dimensional manner to control the oscillatory behavior of the solution, avoiding the procedure of solving any minimization problems or tuning parameters. Extensive convergence comparisons are presented for two different solution gradient computations, identifying the one that satisfies the good neighborhood property for limiting.
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