Computational domain size

Discretize the influence coefficient K x) into a series Kj)2N of size 2N in a region whose sides are twice as that of the computation domain. 

Discretize the pressure functionp(x) into a series pi M of size N in the computation domain, and then extend the length of the series pil into a new series pN )2N through zero padding. 

The solution of the gas flow and temperature fields in the nearnozzle region (as described in the previous subsection), along with process parameters, thermophysical properties, and atomizer geometry parameters, were used as inputs for this liquid metal breakup model to calculate the liquid film and sheet characteristics, primary and secondary breakup, as well as droplet dynamics and cooling. The trajectories and temperatures of droplets were calculated until the onset of secondary breakup, the onset of solidification, or the attainment of the computational domain boundary. This procedure was repeated for all droplet size classes. Finally, the droplets were numerically sieved and the droplet size distribution was determined. 

The initial conditions for the velocity components are set up so that there is a tubular shear layer aligned along the 2 -direction at time t = 0. The tv-velocity has a top-hat profile with a tan-hyperbolic shear layer. Stream wise and azimuthal perturbations are introduced to expedite roll-up and the development of the Widnall instability. The details can be found in [7]. The initial velocity field is made divergence-free using the Helmholtz decomposition. The size of the computational domain (one periodic cubical box) is 4do on each side. 

One of the basic elements of the computational algorithm is the determination of dependent variables at the inlet/outlet boundaries of a computational domain representing a finite length combustor. The essence of the problem lies in the fact that the nonstationary flow field has to be considered throughout a whole (unbounded) physical space, and only in this case the problem is mathematically well-posed. When solving a specific problem numerically, one has to consider a computational domain of a finite size, in which boundary conditions at artificial boundaries are to be imposed. 

Figure 12.2 Application of the nonreflecting bonndary conditions (left part) and standard von Nenmann boundary conditions (right part) in the problem on pressure disturbance propagation in a flow reactor with open left and right boundaries. Time instants (a) 10 /rs, (b) 20 ps, (c) 30 /rs. Flow velocity at the inlet 40 m/s, po = 0.1 MPa, To = 300 K, fco = 9 J/kg, lo = 2 mm. Initial pressure differential Ap/po = 0.5. The size of the computational domain is 3.3 x 2 cm...

The modeling considered 1.25 mm of the channel before the confluence and 3 mm of the channel after the confluence with a plane of symmetry at half the channel depth. The computational domain was discretized with structured hexahedral meshes, the size of the cells being 10 pm long. Diffusion was modeled. 

R. Yamamoto and K Nakanishi, Computer Simulation of Vapor-liquid Phase Separation in two- and three-dimensional Fluids Growth Law of Domain Size, Phys. Rev. B 49 (1994) 14958-14966 II. Domain Structure, Phys. Rev. B 51... 

In the case of the recrystallization progress of the amorphous structure, the determination of the a-Si microstructure is of great importance as an initial phase in the simulations. Many researchers have proposed the preparation methods of fl-Si based on MD simulations and their computer-generated properties were in good agreement with those obtained by experiments. However, details of the microstructures have not yet fully examined [22, 23] because the calculation domain sizes in the ah initio MD simulations were quite limited [24, 25], and the preparation methods of a-Si using various simple empirical inter-atomic potentials involved unphysical treatments. 

The first moment q t) of the structure factor is also computed in order to observe the coarsening processes in the later stage of phase separation more clearly. This quantity q t), the inverse of which is a measure of the average domain size, is defines as... 

The physical interpretation that the particles may introduce a inverse cascade of turbulence has been confirmed numerically by [44] who used direct numerical simulations of arrays of bubbles (12 by 12 and 18 by 18) in 2D low Reynolds number bubbly flows to investigate the relative motion of several bubbles. They found that the bubbles produced eddies much larger than the bubble size. Those eddies kept growing until they were of the same size as the computational domain for the small (12 by 12) array. (For the 18 by 18 array the computation was stopped while the eddies were still growing, and not reached the size of the computational domain). Later studies on the the inverse energy cascade structure of turbulence in bubbly flows and on turbulence structures induced by bubble buoyancy by [106, 107] confirmed the findings of [44]. 

The counterelectrode is placed at a distance B from the working electrode. When UB 1, the solution domain is essentially semi-infinite. Calculations were carried out on a finite domain. Numerical experiments were performed to determine the appropriate size of the truncated computational domain. The required size decreases with increasing Peclet number. 

Table 2.1 Results computed by Teubner and Strey for the data from Ref. [78] with 4>s = volume fraction of the surfactant, = correlation length and d = domain size...

For illustration, let us estimate the dispersion error of the aforementioned narrow-band technique and compare it with the one induced by the wideband method of (2.107)—(2.115). The cell dimensions are chosen as Ay = 2Ax and T2D = 0-85 in (5.46). Figure 5.5 gives the results for two mesh resolutions with respect to Ax. In contrast with the performance of the latter scheme, the narrow-band approach achieves a remarkable reduction around the design frequency, whereas its accuracy deteriorates at finer resolutions. This is, however, not a serious shortcoming, since a given computational domain appears to have a smaller electrical size at lower frequencies and, consequently, the dispersion error is not as considerable as in the high-frequency band. Moreover, it is noteworthy to observe that the narrow-band scheme generates smaller errors for coarser lattices and thus, its application to broadband simulations should not be ruled out. 

The domain of an atmospheric model—that is, the area that is simulated—varies from a few hundred meters to thousands of kilometers (Table 25.1). The computational domain usually consists of an array of computational cells, each having a uniform chemical composition. The size of these cells, that is, the volume over which the predicted concentrations are averaged, determines the spatial resolution of the model. Variation of concentrations at scales smaller than the model resolution cannot easily be resolved. For example, concentration variations over the Los Angeles basin cannot be described by a synoptic scale model that treats the entire area as one computational cell of uniform chemical composition. 

Theories of block copolymers are usually complex, involving computation of the domain size, the interphase thickness between the blocks, the stmc-ture, and the order-disorder transitions. Helfand and Wasserman [1976, 1978, 1980] using the narrow interphase approximation, showed that Eq 4.4 is valid in the limit of infinitely immiscible blocks having (i.e., the strong segrega-... 

The boundary conditions are specified at finite points far from the reaction zone which is in the vicinity of z = 0. The computations presented here were obtained with the boundary conditions imposed atz = 12. There is virtually no effect of further increasing the size of the computational domain. Note that no boundary condition is imposed on Y in the burned region. 

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