遺伝的プログラミングを利用したボルツマン方程式衝突項の近似モデル探索

第51回流体力学講演会/第37回航空宇宙数値シミュレーション技術シンポジウム (2019年7月1日-3日. 早稲田大学早稲田キャンパス国際会議場), 新宿区, 東京

51st Fluid Dynamics Conference / the 37th Aerospace Numerical Simulation Symposium (July 1-3, 2019. International Conference Center, Waseda University), Shinjuku-ku, Tokyo, Japan

The machine learning approach for exploring the approximate analytical description for the collision term in the Boltzmann equation is presented in this paper. Such approximate model is expected to significantly accelerate the numerical simulation of rarefied gas flows without severe degradation in the accuracy. The combination of a genetic programming (GP) method and a nonlinear least square method was adopted for the exploring. Training data was a solution of Direct Simulation Monte Carlo (DSMC) method, which is a stochastic method for rarefied gas dynamics. Considering the separation of the collision term from the translational term in the Boltzmann equation, we only solved the molecular collision by the DSMC method. The numerical solution of the obtained approximate model exhibited almost precise model. But there was still unphysical behavior in the profile of the velocity distribution function. It is suggested that GP may produce the equation including terms with numerical instability and that some restriction should be applied to assure the numerical stability as well as the physical accuracy at the exploring by GP.

形態: カラー図版あり

Physical characteristics: Original contains color illustrations

資料番号: AA1930011011

レポート番号: JAXA-SP-19-007