A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Journal of Computational Physics
High-resolution Burnett simulations of micro Couette flow and heat transfer
Journal of Computational Physics
Boundary conditions for regularized 13-moment-equations for micro-channel-flows
Journal of Computational Physics
Pressure based finite volume method for calculation of compressible viscous gas flows
Journal of Computational Physics
Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
SIAM Journal on Scientific Computing
NR$xx$ Simulation of Microflows with Shakhov Model
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.46 |
The challenge of modeling low-speed rarefied gas flow in the transition regime is well known. In this paper, we propose a numerical solution procedure for the regularized 13 moment equations within a finite-volume framework. The stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first-order approximation. To model confined flows, a complete set of wall boundary conditions for the 13 moment equations are derived based on the Maxwell wall-boundary model. This has been achieved by expanding the molecular distribution function to fourth-order accuracy in Hermite polynomials. Empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation Monte Carlo data. The numerical predictions obtained from the regularized 13 moment equations and the Navier-Stokes-Fourier equations are compared with data generated using the direct simulation Monte Carlo method for planar Couette flow. For a range of wall velocities and Knudsen numbers (0.012-1.0), the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation Monte Carlo data. The results also highlight limitations that are caused by the use of a first-order expansion of the third moment.