Computational Region

A model that employs a two-dimensional cylindrical coordinate system and assumes axial symmetry with respect to r- and z-axes is developed. Figure 3.2.2 shows the coordinate system, computing region, and... 

Computing region, notation of initial and boundary conditions. 

The system of Eq. (6) is written in the dimensionless form using the characteristic values p, p, R, Uj = v PJPi- Then the dimensionless time is t = tj uJRi. The assumption about the flow symmetry enables us to include in the computation region only half of a cylinder or sphere. The cylindrical or spherical geometry of the computation region is assigned by the parameter j = 0 OT 1, the grid steps being Ar and A0, respectively. 

The Newton-Raphson technique Is used since It offers better convergence chan the Gauss-Seldel scheme. There ace, however some limitations to this technique, since the matrix Inversion procedure requires a CPU time approximately proportional to 0(N ) and Che storage Is proportional to N (where N Is Che total number of nodes In the computational region). These factors combine to make Che approach unsuitable for extension to point contact problems where Che number of nodes Is large. 

Thus, the pressure distribution over the computational region was approximated by a series of rectangular regions of constant pressure which allowed the total elastic deformation at the centre of the rectangle to be calculated by the principal of superposition. 

Simulation of the formation of nanoparticles was carried out in a representative volume of calculated with periodic boundary conditions. The computational region for the solution of the above problem is shown in Fig. 4.5. A more detailed statement of the problem and the simulation methodology described in earlier papers [26-29]. 

FIG U RE 4.5 The computational region in the simulation of the formation of nanoparticles by thermal saturation and condensation. 

Fig. 2. Schematic representation of the domain decomposition scheme used to implement flexible Green s function boundary conditions in our GFBC/MGPT atomistic simulation code for dislocation calculations, (a) The three main computational regions separated into a layered

In this case. Maxwell s equations in the main computational region are... 

The electrical heat effects are caused by resistance to current flow, which yields ohmic heating (also called Joule heating). Ohmic heating takes place throughout the solid structure wherever electrical current flows, for instance, from PEN element to interconnect layer. The total ohmic resistance can be decomposed into contributions from various cell components. If the component material has an ohmic resistivity Yj (expressed in m), the ohmic heat generated per unit volume of that computational region can be calculated from... 

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