Direct Simulation Monte Carlo DSMC Method

6 Direct Simulation Monte Carlo (DSMC) Method 

The basic steps during DSMC simulation can be divided into four steps. The total space is divided into cells similar to the finite volume method used in computational fluid dynamics simulation. The size of the DSMC cell is chosen proportional to the mean free path, that is, Ax 2/3. The four steps in DSMC are 

In the second step, the tracking of particles with proper indexing is carried out. The new cell locations of the molecules are indexed properly. In the third step, the collision process is 

In DSMC, there is a long-time requirement for achieving steady state. Let us consider a gas flow in a channel of length 1 mm and height 1 pm with an average speed of 1 mm/s. The convection timescale for the macroscopic disturbance to travel from the inflow to outflow is equal to 1 s. The viscous timescale for the problem is. For air (y = lO m /s), 

Lise 10 s, which is three orders of magnitude less than convective timescale. The mean collision time of air at standard condition is the order of the 10 ° s. Hence, the DSMC step must run about 10 ° time steps for settling to a steady-state condition. 

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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. 

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

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. 

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