Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational Physics
Boundary conditions for regularized 13-moment-equations for micro-channel-flows
Journal of Computational Physics
An h-adaptive mesh method for Boltzmann-BGK/hydrodynamics coupling
Journal of Computational Physics
An Efficient NRxx Method for Boltzmann-BGK Equation
Journal of Scientific Computing
NR$xx$ Simulation of Microflows with Shakhov Model
SIAM Journal on Scientific Computing
Solving the discrete S-model kinetic equations with arbitrary order polynomial approximations
Journal of Computational Physics
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We introduce a numerical method for solving Grad's moment equations or regularized moment equations for an arbitrary order of moments. In our algorithm, we do not explicitly need the moment equations. Instead, we directly start from the Boltzmann equation and perform Grad's moment method [H. Grad, Commun. Pure Appl. Math., 2 (1949), pp. 331-407] and the regularization technique [H. Struchtrup and M. Torrilhon, Phys. Fluids, 15 (2003), pp. 2668-2680] numerically. We define a conservative projection operator and propose a fast implementation, which makes it convenient to add up two distributions and provides more efficient flux calculations compared with the classic method using explicit expressions of flux functions. For the collision term, the BGK model is adopted so that the production step can be done trivially based on the Hermite expansion. Extensive numerical examples for one- and two-dimensional problems are presented. Convergence in moments can be validated by the numerical results for different numbers of moments.