Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation (Communications in Computational Physics, 2018)
The accuracy of moment equations as approximations of kinetic gas theoryis studied for four different boundary value problems. The kinetic setting is given bythe BGK equation linearized around a globally constant Maxwellian using one spacedimension and a three-dimensional velocity space. The boundary value problems includeCouette and Poiseuille flow as well as heat conduction between walls and heatconduction based on a locally varying heating source. The polynomial expansion ofthe distribution function allows for different moment theories of which two popularfamilies are investigated in detail. Furthermore, optimal approximations for a givennumber of variables are studied empirically. The paper focuses on approximationswith relatively low number of variables which allows to draw conclusions in particularabout specific moment theories like the regularized 13-moment equations.