A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics (Communications in Computational Physics, 2014)
An accurate and direct algorithm for solving the semiclassical Boltzmannequation with relaxation time approximation in phase space is presented for paralleltreatment of rarefied gas flows of particles of three statistics. The discrete ordinatemethod is first applied to discretize the velocity space of the distribution function torender 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 ofthe discretized velocity distribution function in physical space and time. The methodis developed for two space dimensions and implemented on gas particles that obeythe Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows arepresented and the results indicating good resolution of the main flow features can beachieved. Flows of wide range of relaxation times and Knudsen numbers coveringdifferent flow regimes are computed to validate the robustness of the method. Therecovery of quantum statistics to the classical limit is also tested for small fugacityvalues.