Hierarchical Reconstruction for Discontinuous Galerkin Methods on Unstructured Grids with a WENO Type Linear Reconstruction
نویسندگان
چکیده
The hierarchical reconstruction [11] is applied to discontinuous Galerkin method on the two-dimensional unstructured grids. We explore a variety of limiter functions used in the construction of piecewise linear polynomials. We show that due to the abrupt shift of stencils, the use of center biased limiter functions is essential in order to recover the desired order of accuracy. Furthermore, we develop a WENO type linear reconstruction in each hierarchical level. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed. We demonstrate that the hierarchical reconstruction can generate essentially non-oscillatory solutions while keeping the resolution and desired order of accuracy for smooth solutions.
منابع مشابه
Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells
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