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

共 40 条

[21] Dynamics of multi -pulse splitting process in one-dimensional Gray -Scott system with fractional order operator
Owolabi, Kolade M.
Karaagac, Berat
CHAOS SOLITONS & FRACTALS, 2020, 136
[22] A new class of efficient one-step contractivity preserving high-order time discretization methods of order 5 to 14
Karouma, Abdulrahman
Truong Nguyen-Ba
Giordano, Thierry
Vaillancourt, Remi
NUMERICAL ALGORITHMS, 2018, 79 (01) : 251 - 280
[23] High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids
Huynh, H. T.
Wang, Z. J.
Vincent, P. E.
COMPUTERS & FLUIDS, 2014, 98 : 209 - 220
[24] High order locally one-dimensional methods for solving two-dimensional parabolic equations
Jianhua Chen
Yongbin Ge
Advances in Difference Equations, 2018
[25] HIGH FIDELITY METHODS FOR MODELING NONLINEAR WAVE PROPAGATION IN ONE-DIMENSIONAL WAVEGUIDES
Liu, Yu
Ghaderi, Pooya
Dick, Andrew J.
INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION - 2012, VOL 4, PTS A AND B, 2013, : 741 - 750
[26] High order locally one-dimensional methods for solving two-dimensional parabolic equations
Chen, Jianhua
Ge, Yongbin
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[27] A High-Order Arbitrary Lagrangian-Eulerian Oscillation-Free Discontinuous Galerkin Scheme for One-Dimensional Compressible Multi-Material Flows
Zhao, Xiaolong
Yu, Xijun
Song, Shicang
Zou, Shijun
Qing, Fang
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2025,
[28] A high-order physical-constraints-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin scheme for one-dimensional compressible multi-material flows
Zhao, Xiaolong
Yu, Xijun
Qing, Fang
Zou, Shijun
PHYSICS OF FLUIDS, 2024, 36 (11)
[29] Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case
Zhu, Hongqiang
Qiu, Jianxian
JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (18) : 6957 - 6976
[30] Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics
Al Jahdali, R.
Dalcin, L.
Boukharfane, R.
Nolasco, I. R.
Keyes, D. E.
Parsani, M.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2022, 118 : 1 - 17

← 1 2 3 4 →