A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case

被引：7

作者：

Reyes, Adam ^{[1
]}

Lee, Dongwook ^{[2
]}

Graziani, Carlo ^{[3
]}

Tzeferacos, Petros ^{[3
,4
]}

机构：

[1] Univ Calif Santa Cruz, Dept Phys, Santa Cruz, CA 95064 USA

[2] Univ Calif Santa Cruz, Appl Math & Stat, Santa Cruz, CA 95064 USA

[3] Univ Chicago, Dept Astron & Astrophys, Flash Ctr Computat Sci, Chicago, IL 60637 USA

[4] Univ Oxford, Dept Phys, Oxford, England

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 76卷 / 01期

基金：

美国国家科学基金会;

关键词：

Gaussian processes; Stochastic models; High-order methods; Finite volume method; Gas dynamics; Magnetohydrodynamics; FINITE-VOLUME METHOD; RADIAL BASIS FUNCTIONS; EFFICIENT IMPLEMENTATION; POSTSHOCK OSCILLATIONS; CONSERVATION-LAWS; RIEMANN PROBLEMS; EQUATIONS; SCHEMES; INTERPOLATION; ACCURATE;

D O I：

10.1007/s10915-017-0625-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an entirely new class of high-order methods for computational fluid dynamics based on the Gaussian process (GP) family of stochastic functions. Our approach is to use kernel-based GP prediction methods to interpolate/reconstruct high-order approximations for solving hyperbolic PDEs. We present a new high-order formulation to solve (magneto)hydrodynamic equations using the GP approach that furnishes an alternative to conventional polynomial-based approaches.

引用

页码：443 / 480

页数：38

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