A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta Discontinuous Galerkin Methods
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A different WENO limiting strategy using immediate neighbors by dividing them into subcells for the Discontinuous Galerkin method has been proposed. In this limiter, we reconstruct the polynomial in the cell where limiting is needed, using a WENO reconstruction polynomial with an appropriate stencil consisting of only the immediate neighbors. The immediate neighbors are divided into the required stencil and an existing WENO limiting strategy is used. This is termed as compact subcell WENO limiter or CSWENO limiter in short. This is quite effective as the Discontinuous Galerkin method uses only immediate neighbors for the solution of a given equation. Accuracy tests and results for one-dimensional and two-dimensional Burgers equation and one-dimensional and two-dimensional Euler equations for Cartesian meshes are presented using this limiter. Comparisons with the parent WENO limiter are provided wherever appropriate and the performance of the current limiter is found to be slightly better than the parent WENO limiter for higher orders.
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