Coupling kinetic and continuum using data-driven maximum entropy distribution

JOURNAL OF COMPUTATIONAL PHYSICS

卷:444

Article

Sadr, Mohsen^1,2  Wang, Qian²  Gorji, M. Hossein³ 

[1] Rhein Westfal TH Aachen, Appl & Computat Math, Schinkestr 2, D-52062 Aachen, Germany

[2] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland

[3] Empa, Swiss Fed Labs Mat Sci & Technol, Lab Multiscale Studies Bldg Phys, Dubendorf, Switzerland

关键词: Maximum entropy distribution;    Gaussian process;    Artificial Neural Network;    Coupling continuum and kinetic scales;   

DOI  :  10.1016/j.jcp.2021.110542

来源: Elsevier

【 摘 要 】

An important class of multi-scale flow scenarios deals with an interplay between kinetic and continuum phenomena. While hybrid solvers provide a natural way to cope with these settings, two issues restrict their performance. Foremost, the inverse problem implied by estimating distributions has to be addressed, to provide boundary conditions for the kinetic solver. The next issue comes from defining a robust yet accurate switching criterion between the two solvers. This study introduces a data-driven kinetic-continuum coupling, where the Maximum-Entropy-Distribution (MED) is employed to parametrize distributions arising from continuum field variables. Two regression methodologies of Gaussian-Processes (GPs) and Artificial-Neural-Networks (ANNs) are utilized to predict MEDs efficiently. Hence the MED estimates are employed to carry out the coupling, besides providing a switching criterion. To achieve the latter, a continuum breakdown parameter is defined by means of the Fisher information distance computed from the MED estimates. We test the performance of our devised MED estimators by recovering bi-modal densities. Next, MED estimates are integrated into a hybrid kinetic-continuum solution algorithm. Here Direct Simulation Monte-Carlo (DSMC) and Smoothed-Particle Hydrodynamics (SPH) are chosen as kinetic and continuum solvers, respectively. The problem of monatomic gas inside Sod's shock tube is investigated, where DSMC-SPH coupling is realized by applying the devised MED estimates. Very good agreements with respect to benchmark solutions along with a promising speed-up are observed in our reported test cases. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free