Application of the kinetic and continuum Techniques to the multi-scale flows in MEMS Devices

A hybrid particle approach for continuum and rarefied flow simulation

“…In these ''all-particle" hybrid algorithms, macroscopic flow properties are calculated in both rarefied and continuum regions by averaging quantities among representative particles, and DSMC collision calculations are replaced in continuum regions by procedures which involve redistributing particle velocities under an assumption of local thermal equilibrium. Particle velocities are redistributed either through the use of a DSMC collision limiter scheme [13,14], or through direct resampling from a Maxwellian distribution at the cell-averaged temperature and bulk velocity [10,11]. While such hybrid techniques are far easier to implement than coupled CFD-DSMC algorithms and provide a simple solution to the interface scatter problem in CFD-DSMC algorithms, these all-particle hybrid techniques are prone to large errors associated with numerical diffusion.…”

“…With these goals in mind, some authors have proposed hybrid simulation approaches which use DSMC type particles throughout the simulation domain [10,11,13,14]. In these ''all-particle" hybrid algorithms, macroscopic flow properties are calculated in both rarefied and continuum regions by averaging quantities among representative particles, and DSMC collision calculations are replaced in continuum regions by procedures which involve redistributing particle velocities under an assumption of local thermal equilibrium.…”

“…In general, such techniques are either intended only for limited types of flows and certain modes of nonequilibrium [18,19], or are very computationally expensive and inappropriate for use in simulation methods which include near-equilibrium assumptions [20]. A comparative analysis of different breakdown criteria is out of the scope of the present study, and the reader is referred to an extensive body of existing research on this topic [11,12,14,[18][19][20]. For the hybrid algorithm presented here, a relatively simple and conservative technique is therefore proposed.…”

A low diffusion particle method for simulating compressible inviscid flows

“…While a number of published equilibrium particle methods have shown promise for compressible inviscid flow simulation [3][4][5][6][7], these methods are in general considerably less practical or desirable than CFD methods commonly used to simulate this type of flow. One major problem with existing equilibrium particle methods is their tendency to suffer from large numerical diffusion errors, including effects of artificial viscosity, thermal conductivity, and mass diffusion.…”

“…In contrast, equilibrium particle methods are intended specifically for continuum flow simulation, and differ from DSMC primarily in procedures for updating particle velocities during each time step. In place of simulated binary collisions involving some fraction of particles in each cell, all particles may experience multiple collisions per time step -as in DSMC collision limiter schemes [3][4][5] -or collision procedures may be replaced by a resampling step, where new particle velocities are sampled from a Maxwellian distribution in such a way that total momentum and energy are conserved [6,7]. By enforcing local thermal equilibrium in every cell during each time step, these methods effectively reproduce characteristics of the Boltzmann equation at the equilibrium limit, and are assumed to provide results equivalent to a numerical solution of the compressible Euler equations.…”