A variable high-order shock-capturing finite difference method with GP-WENO

作     者：Reyes, Adam Lee, Dongwook Graziani, Carlo Tzeferacos, Petros 

作者机构：Department of Physics University of California Santa CruzCA United States Department of Applied Mathematics University of California Santa CruzCA United States Flash Center for Computational Science Department of Astronomy & Astrophysics University of Chicago IL United States Mathematics and Computer Science Argonne National Laboratory ArgonneIL United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Gaussian distribution 

摘      要：We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is an extension of the GP high-order method originally introduced in a finite volume framework by the same authors. The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. For shocks and discontinuities, this GP interpolation scheme uses a nonlinear shock handling strategy similar to Weighted Essentially Non-oscillatory (WENO), with a novelty consisting in the fact that nonlinear smoothness indicators are formulated in terms of the Gaussian likelihood of the local stencil data, replacing the conventional L2-type smoothness indicators of the original WENO method. We demonstrate that these GP-based smoothness indicators play a key role in the new algorithm, providing significant improvements in delivering high - and selectable - order accuracy in smooth flows, while successfully delivering non-oscillatory solution behavior in discontinuous flows. Copyright © 2018, The Authors. All rights reserved.