Boundary Closures for ESWENO Schemes

Mark Carpenter
NASA Langley Research Center
Hampton, Virginia, USA


Weighted Essentially NonOscillatory (WENO) schemes are routinely used to perform high resolution simulations of canonical problems containing discontinuities. Because conventional WENO formulations rely on structured meshes, extension to complex geometries is problematic. We present a systematic plan and show progress towards a general multi-block WENO capability. To date, Energy Stable WENO (ESWENO) finite difference schemes have been developed for orders up to eight, that are L_2 stable for both continuous and discontinuous solutions of linear hyperbolic systems on period domains. To partially address the open question 'How are multiple domains coupled, while retaining all the ESWENO properties?' a fully fourth-order, finite-domain ESWENO formulation is developed, featuring new boundary closures that maintain design accuracy, conservation and L_2 stability, while accommodating full WENO stencil biasing. Test cases are presented that demonstrate the efficacy of the new approach.