Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation  

作　　者：Qin Li Xu Yang 

机构地区：[1]Department of Mathematics,University of Wisconsin,Madison,WI 53706,USA [2]Department of Mathematics,University of California,Santa Barbara,CA 93106-3080,USA

出　　处：《Communications in Computational Physics》2014年第4期996-1011,共16页计算物理通讯（英文）

基　　金：supported by the NSF grant DMS-1114546 and NSF Research Network in Mathematical Sciences“KI-Net:Kinetic description of emerging challenges in multiscale problems of natural sciences”;X.Y.was partially supported by the startup funding of University of California,Santa Barbara。

摘　　要：This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared to the single species Boltzmann equation that the method was originally applied on,this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species.Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number.We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples.

关 键 词：Multispecies Boltzmann equation exponential Runge-Kutta method hydrodynamic limit asymptotic preserving property positivity preserving 

分 类 号：O17[理学—数学]