Convergent High-Order Compact WENO Discontinuity Capturing with Positivity Preserving for Unstructured Discontinuous Galerkin Schemes

Recent investigation revealed that the more advanced discontinuity capturing weighted essentially nonoscillatory (WENO) technique, which is of high-order and guarantees the formal order of accuracy in the smooth regions, is nonconvergent (see the image on the right) and a compact convergent WENO for DG has not been developed. Approach: Development of compact convergent WENO for unstructured DG schemes with construction of a set of polynomials that have different lengths than the original polynomials. Innovation: The innovation is in the development and construction of compact high-order WENO scheme that is convergent for energetic discontinuities along with a positivity preserving scheme to guarantee density and pressure values remain within physical range.

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