Direct Simulation Monte Carlo DSMC

Since the middle of the 1990s, another computation method, direct simulation Monte Carlo (DSMC), has been employed in analysis of ultra-thin film gas lubrication problems [13-15]. DSMC is a particle-based simulation scheme suitable to treat rarefied gas flow problems. It was introduced by Bird [16] in the 1970s. It has been proven that a DSMC solution is an equivalent solution of the Boltzmann equation, and the method has been effectively used to solve gas flow problems in aerospace engineering. However, a disadvantageous feature of DSMC is heavy time consumption in computing, compared with the approach by solving the slip-flow or F-K models. This limits its application to two- or three-dimensional gas flow problems in microscale. In the... 

Understanding the dependence of film structure and morphology on system layout and process parameters is a core topic for the further development of ZnO technology. Work is being performed on in situ characterization of deposition processes. Growth processes are simulated using Direct Simulation Monte-Carlo (DSMC) techniques to simulate the gas flow and sputter kinetics simulation and Particle-ln-Cell Monte-Carlo (PICMC) techniques for the plasma simulation [132]. 

Modified Navier-Stokes equations are also used by [10] in the range of 0.01 < Kn < 30 and the results are eompared to Direct Simulation Monte Carlo (DSMC) and linearized Boltzman solutions. They obtained good results for the centerline velocity, assuming b = -1, but deviations for the slip veloeity for 0.1 < Kn < 5. 

The Boltzmann equation is solved by the particulate methods, the Molecular Dynamics (MD), the Direct Simulation Monte Carlo (DSMC) method, or by deriving higher order fluid dynamics approximations beyond Navier-Stokes, which are the Burnett Equations. The Burnett equation... 

Figure4.6 Left a microfluidicftlterexample.The baths are simulated by using the continuum Stokes equations and the filter is simulated by using the direct simulation Monte Carlo (DSMC) method. Right plot of temperature in the device...

One of the earliest particle-based schemes is the Direct Simulation Monte Carlo (DSMC) method of Bird [126]. In DSMC simulations, particle positions and velocities are continuous variables. The system is divided into cells and pairs of particles in a cell are chosen for collision at times that are determined from a suitable distribution. This method has seen wide use, especially in the rarefied gas dynamics community where complex fluid flows can be simulated. 

Diffusive flow for neutrals The importance of convective vs. diffusive flow of neutrals is determined by the Peclet number Pe = uL/D, where L is a characteristic dimension of the system. Away from inlet and exit ports, the characteristic length will be on the order of the reactor dimension. The system will be primarily diffusive when Pe 1. For CI2 gas in a reactor with L 0.1 m and a neutral species diffusivity of D 5m s at 20mtorr, the Peclet number will be Pe 1 when M = 50ms. Convective gas velocities are not likely to be that high, except for a small region near the gas inlet ports. It follows that gas flow can be approximated as diffusive this obviates the need for solving the full Navier-Stokes equations which adds to the computational burden. It should be noted that both the diffusivity and the convective velocity scale inversely with gas pressure, so the Pe number is independent of pressure. However, as the pressure is lowered to the point of free molecular flow, the gas diffusion coefficient has no meaning any more. Direct Simulation Monte Carlo (DSMC) [41, 143] can then be applied to solve for the fluid velocity profiles. 

Direct simulation Monte Carlo (DSMC) method is a statistical approach widely employed for simulating rarefied micro-/nanoflows. DSMC is... 

Direct-Simulation Monte Carlo (DSMC) Method... 

In microfluid mechanics, the direct simulation Monte Carlo (DSMC) method has been applied to study gas flows in microdevices [2]. DSMC is a simple form of the Monte Carlo method. Bird [3] first applied DSMC to simulate homogeneous gas relaxation problem. The fundamental idea is to track thousands or millions of randomly selected, statistically representative particles and to use their motions and interactions to modify their positions and states appropriately in time. Each simulated particle represents a number of real molecules. Collision pairs of molecule in a small computational cell in physical space are randomly selected based on a probability distribution after each computation time step. In essence, particle motions are modeled deterministically, while collisions are treated statistically. The backbone of DSMC follows directly the classical kinetic theory, and hence the applications of this method are subject to the same limitations as kinetic theory. 

Noncontinuous approach can be deterministic or stochastic. In deterministic approaches, such as the molecular dynamics (MD) method and the lattice Boltzmann method (LBM), the particle or molecule s trajectory, velocity, and intermolecular collision are calculated or simulated in a deterministic manner. In the stochastic approaches, such as the direct simulation Monte Carlo (DSMC) method, randomness is introduced into the solution variables. 

However, for Knudsen numbers higher than unity, as it could be the case in nanochaimels (gas flow in nanochannels) or in low-pressure flows in microchannels, the continuum approach is no longer valid, and molecular methods such as the Direct Simulation Monte Carlo - DSMC - (Monte Carlo method) or the Lattice Boltzmann methods (Lattice Boltzmann method) should be used. 

Alexeenko et al. [9, 10] have performed non-continuum Direct Simulation Monte Carlo (DSMC) analyses of milli-/micro-nozzle flows in order to examine the influence of rarefaction effects on performance. The DSMC method is a statistical approach to the solution of the Boltzmann equation, the governing equation for rarefied gasdynam-ics. Their work has found that for Knudsen numbers of Kn 0.1, gas-surface interactions have a strong influence on the flow in both the converging and diverging sections... 

In the transition regime, the molecularly based Boltzmann equation cannot easily be solved unless the nonlinear collision integral is simplified. MD solution as mentioned earlier is not suitable/or dilute gases. The best approach for the transition regime is the direct simulation Monte Carlo (DSMC). This approach is introduced in a later section. 

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