Stability Analysis Of Diffusive Relaxation Schemes For Multiscale Discrete-Velocity Kinetic Equations

Kinetic equations are widely used in many areas.The relaxation parameter exists inmany kinetic models of the Boltzmann equation, which may be large or small.In onecomputational domain,when the relaxation parameter is small,we require the time stepto be much larger for numerical efficiency.But in some circumstances,large scale ofrelaxation parameter exist.Some theories have been developed before. Most of them are focused on thesituation that relaxation parameter is small but did not give a complete discussion ofstabiliy for all range of the relaxation parameter.This paper gives a consistent stabilityregion with different scale of relaxation parameter for two schemes and compare them.This paper focuses on the JPT scheme[5] and K scheme[7].First of all,we apply themethods (named JPT scheme and K scheme) to the equation in the paper,which.Afterthat,we use the Fourier method to get the stability condition and analyze theirdifferences.At last,we improve the current schemes with a better stability property.