Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Rarefied flow computations using nonlinear model Boltzmann equations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
High order numerical methods for the space non-homogeneous Boltzmann equation
Journal of Computational Physics
Study on gas kinetic unified algorithm for flows from rarefied transition to continuum
Journal of Computational Physics
Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
Journal of Computational Physics
Monte Carlo solution of the Boltzmann equation via a discrete velocity model
Journal of Computational Physics
Numerical properties of high order discrete velocity solutions to the BGK kinetic equation
Applied Numerical Mathematics
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A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier---Stokes and DSMC solutions.