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Numerical Error Analysis for Deterministic Kinetic Solutions of Low-Speed Flows
 

Summary: Numerical Error Analysis for Deterministic Kinetic
Solutions of Low-Speed 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 noise-to-signal ratio and a longer time to reach the steady state. For such low-speed
flows, the discrete-ordinate solution of kinetic model equations can provide accurate and computationally efficient numerical
modeling. In this work, analysis of the numerical errors of discrete-ordinate solution of the kinetic model equation is
carried out using the Richardson extrapolation on non-uniform meshes. The procedure is illustrated for a second-order finite-
difference solution of ellipsoidal statistical kinetic model equation for a two-dimensional low-speed rarefied flow generated
by a non-uniformly 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 steady-state; (b) larger sample sizes to attain a
required signal-to-noise 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
high-aspect ratio geometries can not be implemented in an atomistic simulation. Last but not least, there are inher-

  

Source: Alexeenko, Alina - School of Aeronautics and Astronautics, Purdue University

 

Collections: Engineering