New High-order Methods using Gaussian Processes for Computational Fluid Dynamics Simulations

11th International Conference on Numerical Modeling of Space Plasma Flows

Lee, Dongwook^1 ; Reyes, Adam^2 ; Graziani, Carlo^3 ; Tzeferacos, Petros^3,4

Applied Mathematics and Statistics, University of California, Santa Cruz

CA, United States^1

Department of Physics, University of California, Santa Cruz

CA, United States^2

Flash Center for Computational Science, Department of Astronomy and Astrophysics, University of Chicago, IL, United States^3

Physics, Oxford University, United Kingdom^4

关键词: Computational fluid dynamics simulations;    Covariance kernel;    Gaussian probability distributions;    Gaussian Processes;    High-order approximation;    High-order methods;    Numerical algorithms;    Prediction techniques;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/837/1/012018/pdf
DOI  :  10.1088/1742-6596/837/1/012018

来源: IOP

【 摘 要 】

We present an entirely new class of high-order numerical algorithms for computational fluid dynamics simulations. The new method is based on the Gaussian Processes (GP) modeling that generalizes the Gaussian probability distribution. Our approach is to adapt the idea of the GP prediction technique that utilizes the covariance kernel functions, and use the GP prediction to interpolate/reconstruct a high-order approximations for solving hyperbolic PDEs. We propose the GP high-order method as a new class of numerical high-order formulations, alternative to the conventional polynomial-based approaches.