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A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics

Published online by Cambridge University Press:  03 June 2015

Jaw-Yen Yang ,
Bagus Putra Muljadi ,
Zhi-Hui Li  and
Han-Xin Zhang
Jaw-Yen Yang*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan
Bagus Putra Muljadi*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan FCS STAE, Université Paul Sabatier, Institut de mathématiques de Toulouse, Toulouse 31400, France
Zhi-Hui Li*
Affiliation:
National Laboratory for Computational Fluid Dynamics, Beijing 100191, China China Aerodynamics Research and Development Center, Mianyang, 621000, China
Han-Xin Zhang*
Affiliation:
National Laboratory for Computational Fluid Dynamics, Beijing 100191, China China Aerodynamics Research and Development Center, Mianyang, 621000, China
*
Corresponding author.Email:yangjy@iam.ntu.edu.tw
Email:muljadi.bp@gmail.com
Email:zhli0097@x263.net
Email:hanxinzhang@tom.com
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Abstract

An accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time. The method is developed for two space dimensions and implemented on gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows are presented and the results indicating good resolution of the main flow features can be achieved. Flows of wide range of relaxation times and Knudsen numbers covering different flow regimes are computed to validate the robustness of the method. The recovery of quantum statistics to the classical limit is also tested for small fugacity values.

Keywords

82-0882B3082B4035Q20Semiclassical Boltzmann-BGK equationweighted essentially non-oscillatorydiscrete ordinate method

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 1 , July 2013 , pp. 242 - 264
Copyright
Copyright © Global Science Press Limited 2013

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