Thursday, Feb 1, 2018 - 3:30pm-Allen 14
This Colloquium is cancelled.
Hybrid compact-WENO finite difference scheme with radial basis function based shock detection method for hyperbolic conservation laws
Dr. Wai-Sun Don
Title: Hybrid compact-WENO finite difference scheme with radial basis function based shock detection method for hyperbolic conservation laws
Abstract: Hybrid scheme, based on the high order nonlinear characteristic-wise weighted essentially non-oscillatory (WENO) conservative finite difference scheme and the spectral-like linear compact finite difference scheme, has been developed for capturing shocks and strong gradients accurately and resolving fine scale structures efficiently for hyperbolic conservation laws. The key issue in any hybrid scheme is the design of an accurate, robust, and efficient high order shock detection algorithm which is capable of determining the smoothness of the solution at any given grid point and time. An improved iterative adaptive multi-quadric radial basis function (IAMQ-RBF-Fast) method has been successfully developed as an edges detector of the piecewise smooth functions. In this study, we address and resolve several technical challenges with state-of-arts numerical techniques, such as reducing the ill-condition of the large Toeplitz matrix system via domain rescaling, improving the efficiency of finding the inverse of Toeplitz matrix via the recursive Levinson-Durbin method and domain decomposition, increasing the robustness of the shock detection algorithm by employing the Tukey's boxplot method, yielding an accurate, robust and efficient RBF shock detection method. The applicability and performance of the RBF edge detection method as the shock detector in the hybrid scheme in terms of accuracy, robustness, efficiency, resolution and other implementation issues is studied in detail. Several one- and two-dimensional benchmark problems in shocked flow demonstrate that the proposed hybrid scheme can reach a speedup of the CPU times by a factor up to 2-3 compared with the pure fifth order WENO-Z scheme.