The method provides selectable high-order accuracy by employ-ing a kernel-based Gaussian Process (GP) data prediction method which is an extensionof the GP high-order method originally introduced in a finite volume framework by thesame authors. We present a new finite di ff erence shock-capturing scheme for hyperbolic equations onstatic uniform grids. 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.ĪA variable high-order shock-capturing finite di ff erencemethod with GP-WENO Adam Reyes a, Dongwook Lee b, ∗, Carlo Graziani d, Petros Tzeferacos c a Department of Physics, The University of California, Santa Cruz, CA, United States b Department of Applied Mathematics, The University of California, Santa Cruz, CA, United States c Flash Center for Computational Science, Department of Astronomy & Astrophysics, The University ofChicago, IL, United States d Mathematics and Computer Science, Argonne National Laboratory, Argonne, IL, United States type smoothness indicators of the original WENO method. 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 The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. 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.
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids.
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