An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation
An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation
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DOI：
10.2140/camcos.2022.17.1
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发表时间：
2020-03
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影响因子：
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通讯作者：
Steven I. Reeves;Dongwoo Lee;A. Reyes;C. Graziani;P. Tzeferacos
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作者：
Steven I. Reeves;Dongwoo Lee;A. Reyes;C. Graziani;P. Tzeferacos
提出了一种新的无多项式延拓方法，用于可压缩和不可压缩计算流体动力学的自适应网格细化（AMR）模拟。新方法是使用多维核高斯过程（GP）延长模型。该方案的公式化受到了A. Reyes等人（A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling，Journal of Scientific Computing，76（2017），443-480; A variable high-order shock-capturing finite difference method with GP-WENO，Journal of Computational Physics，381（2019），189-217）。在本文中，我们扩展了以前的GP插值和重建的一个新的基于GP的AMR延长方法，提供了一个高阶精确的扩展数据从粗到细的网格AMR网格层次。在可压缩流动模拟中，必须特别注意以稳定的方式处理激波和间断。为了满足这一点，我们利用冲击处理策略，使用基于GP的平滑度指标，在以前的GP工作由A。Reyes等人，我们使用AMReX库证明了GP-AMR方法在一系列测试套件问题中的有效性，其中GP-AMR方法已经实现。
We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the GP methods introduced by A. Reyes et al. (A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A variable high-order shock-capturing finite difference method with GP-WENO, Journal of Computational Physics, 381 (2019), 189-217). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR prolongation method that delivers a high-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations special care is necessary to handle shocks and discontinuities in a stable manner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We demonstrate the efficacy of the GP-AMR method in a series of testsuite problems using the AMReX library, in which the GP-AMR method has been implemented.