Friday, February 17, 2012

1202.3624 (Zhenning Cai et al.)

The NRxx Method for Polyatomic Gases    [PDF]

Zhenning Cai, Ruo Li
In this paper, we propose a numerical regularized moment method to solve the
Boltzmann equation with ES-BGK collision term to simulate polyatomic gas flows.
This method is an extension to the polyatomic case of the method proposed in
[9], which is abbreviated as the NRxx method in [8]. Based on the form of the
Maxwellian, the Laguerre polynomials of the internal energy parameter are used
in the series expansion of the distribution function. We develop for polyatomic
gases all the essential techniques needed in the NRxx method, including the
efficient projection algorithm used in the numerical flux calculation, the
regularization based on the Maxwellian iteration and the order of magnitude
method, and the linearization of the regularization term for convenient
numerical implementation. Meanwhile, the particular integrator in time for the
ES-BGK collision term is put forward. The shock tube simulations with Knudsen
numbers from 0.05 up to 5 are presented to demonstrate the validity of our
method. Moreover, the nitrogen shock structure problem is included in our
numerical experiments for Mach numbers from 1.53 to 6.1.
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