 
Summary: Numerical Error Analysis for Deterministic Kinetic
Solutions of LowSpeed Flows
Alina A. Alexeenko
School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907.
Abstract. The computational cost of the direct simulation Monte Carlo solutions of rarefied flows increases with decreasing
average flow velocity due to larger noisetosignal ratio and a longer time to reach the steady state. For such lowspeed
flows, the discreteordinate solution of kinetic model equations can provide accurate and computationally efficient numerical
modeling. In this work, analysis of the numerical errors of discreteordinate solution of the kinetic model equation is
carried out using the Richardson extrapolation on nonuniform meshes. The procedure is illustrated for a secondorder finite
difference solution of ellipsoidal statistical kinetic model equation for a twodimensional lowspeed rarefied flow generated
by a nonuniformly heated plate.
INTRODUCTION
Starting from the pioneering work by Bird in early 1960s[1] on the development of stochastic numerical methods for
kinetic description of gas flows, the direct simulation Monte Carlo (DSMC) method has evolved into a powerful numer
ical tool that has provided accurate and efficient solutions to many important problems of rarefied gas dynamics.[2, 3]
However, the computational cost of the DSMC method increases with decreasing Mach number due to: (a) explicit time
integration in the DSMC algorithm and, therefore, long time to reach a steadystate; (b) larger sample sizes to attain a
required signaltonoise ratio when the average gas velocity is small in comparison to thermal speed[4]. Additionally,
coordinate transformation in physical space domain that could have greatly increased computational efficiency for a
highaspect ratio geometries can not be implemented in an atomistic simulation. Last but not least, there are inher
