We construct an efficient numerical scheme for the quantum Fokker-Planck-Landau(FPL)equation that works uniformly from kinetic to fluid regimes.Such a scheme inevitably needs an implicit discretization of the nonlinea...We construct an efficient numerical scheme for the quantum Fokker-Planck-Landau(FPL)equation that works uniformly from kinetic to fluid regimes.Such a scheme inevitably needs an implicit discretization of the nonlinear collision operator,which is difficult to invert.Inspired by work[9]we seek a linear operator to penalize the quantum FPL collision term QqFPL in order to remove the stiffness induced by the small Knudsen number.However,there is no suitable simple quantum operator serving the purpose and for this kind of operators one has to solve the complicated quantum Maxwellians(Bose-Einstein or Fermi-Dirac distribution).In this paper,we propose to penalize QqFPL by the”classical”linear Fokker-Planck operator.It is based on the observation that the classicalMaxwellian,with the temperature replaced by the internal energy,has the same first five moments as the quantum Maxwellian.Numerical results for Bose and Fermi gases are presented to illustrate the efficiency of the scheme in both fluid and kinetic regimes.展开更多
基金supported by NSF grant DMS-0608720 and NSF FRG grant DMS-0757285.S.
文摘We construct an efficient numerical scheme for the quantum Fokker-Planck-Landau(FPL)equation that works uniformly from kinetic to fluid regimes.Such a scheme inevitably needs an implicit discretization of the nonlinear collision operator,which is difficult to invert.Inspired by work[9]we seek a linear operator to penalize the quantum FPL collision term QqFPL in order to remove the stiffness induced by the small Knudsen number.However,there is no suitable simple quantum operator serving the purpose and for this kind of operators one has to solve the complicated quantum Maxwellians(Bose-Einstein or Fermi-Dirac distribution).In this paper,we propose to penalize QqFPL by the”classical”linear Fokker-Planck operator.It is based on the observation that the classicalMaxwellian,with the temperature replaced by the internal energy,has the same first five moments as the quantum Maxwellian.Numerical results for Bose and Fermi gases are presented to illustrate the efficiency of the scheme in both fluid and kinetic regimes.
基金国家自然科学基金(批准号:1117122811231006+6 种基金1146116100711225102和11301094)国家自然科学基金国际(地区)合作与交流项目NSFC-RGC项目(中国香港)(批准号:N-City U 102/12)北京市长城学者项目(批准号:CIT&TCD20140323)北京市博士后基金(批准号:2014ZZ-96)广西省自然科学基金(批准号:2014GXNSFBA118020)广西大学科研基金(批准号:XBZ130086)资助项目
