Boundary element method model calculations

To calculate free energies of solvation for several organic molecules, Fortunelli and Tomasi applied the boundary element method for the reaction field in DFT/SCRF framework173. The authors demonstrated that the DFT/SCRF results obtained with the B88 exchange functional and with either the P86 or the LYP correlation functional are significantly closer to the experimental ones than the ones steming from the HF/SCRF calculations. The authors used the same cavity parameters for the HF/SCRF and DFT/SCRF calculations, which makes it possible to attribute the apparent superiority of the DFT/SCRF results to the density functional component of the model. The boundary element method appeared to be very efficient computationally. The DFT/SCRF calculations required only a few percent more CPU time than the corresponding gas-phase SCF calculations. 

Kawamoto (2) developed a two-dimensional model that is based on a double iterative boundary element method. The numerical method calculates the secondary current distribution and the current distribution within anisotropic resistive electrodes. However, the model assumes only the initial current distribution and does not take into account the effect of the growing deposit. Matlosz et al. (3) developed a theoretical model that predicts the current distribution in the presence of Butler-Volmer kinetics, the current distribution within a resistive electrode and the effect of the growing metal. Vallotton et al. (4) compared their numerical simulations with experimental data taken during lead electrodeposition on a Ni-P substrate and found limitations to the applicability of the model that were attributed to mass transfer effects. 

Many different numerical methods can be used to calculate the ship squat. Their only common point is that they calculate the velocity components and the pressure of the flow surrounding the ship. Depending on whether the fluid is modeled as viscous, a potential velocity function can be used or a more sophisticated flow model has to be applied. Some models are based on slender body theory, whereas others use the boundary elements method (BEM) or the finite element method (FEM). 

The BEM is really based on a particiflar numerical resolution. It is commonly applied for wave-resistance calciflations using Green s function to calculate the potential velocity function. Derivatives of the potential velocity function give the velocity components in Cartesian coordinates. Biihring made a squat model called fast boundary elements method (FBEM) based on this boundary element method. The reliability of the model has to be verified, however, as no comparisons with ship squat measurements was foimd. 

Stress calculations are carried out by the finite element method. Here, the commercial finite method code ABAQUS (Hibbit, Karlsson, and Sorensen, Inc.) is used. Other codes such as MARC, ANSYS are also available. To calculate the stresses precisely, appropriate meshes and elements have to be used. 2D and shell meshes are not enough to figure out stress states of SOFC cells precisely, and thus 3D meshes is suitable for the stress calculation. Since the division of a model into individual tetrahedral sometimes faces difficulties of visualization and could easily lead to errors in numbering, eight-comered brick elements are convenient for the use. The element type used for the stress simulation here is three-dimensional solid elements of an 8-node linear brick. In the coupled calculation between the thermo-fluid calculation and the stress calculation a same mesh model have to be used. Consequently same discrete 3D meshes used for the thermo-fluid analysis are employed for the stress calculation. Using ABAQUS, the deformations and stresses in a material under a load are calculated. Besides this treatment, the initial and final conditions of models can be set as the boundary conditions and the structural change can thus be treated. 

ABSTRACT In this paper, established the mathematical model of the process of thermal storage in the solar-ground concrete pile. It adopted finite element methods to numerically simulate the unsteady-state temperature field of concrete pile that around the underground vertical tube, given the calculated format of different boundary condition, analyzed the temperature variation rule of the concrete around heat exchanger. This paper provided reference basis of ascertain method about the bury depth of the vertical U-tube and the mix proportion of the concrete pile. 

Although accurate values of the optical properties of magnetic lenses can be obtained only by numerical methods, in which the field distribution is first calculated by one of the various techniques available—finite differences, finite elements, and boundary elements in particular—their variation can be studied with the aid of field models. The most useful (though not the most accurate) of these is Glaser s bell-shaped model, which has the merits of simplicity, reasonable accuracy, and, above all, the possibility of expressing all the optical quantities such as focal length, focal distance, the spherical and chromatic aberration coefficients Cg and Q, and indeed all the third-order aberration coefficients, in closed form, in terms of circular functions. In this model, 5(z) is represented by... 

In the same year, Weil et al. [13] introduced a sealing concept for planar SOFCs. The finite element method (FEM) was used to aid in scaling up a bonded compliant sealant design to a 120 x 120 mm component. The stresses of the cell, foil, brazes, and frame were calculated and compared with experimental fracture and yield stress results. A quarter symmetrical model was used. The commercial software AN SYS was utilized. The tensile stress of the component was predicted, considering thermal cycling from elevated temperature to room temperature. The materials used were mentioned, but no properties were given. Regarding the structural analysis boundary conditions and the failure criteria employed, material models were not depicted. 

In the FEM calculation, software is used that operates on the finite element method. A data model of the mold or a mold part is read into the software. The data model also includes the part contour. Under certain conditions (cavity temperature, melt temperature, etc.), a temperature control layout is designed around the molded part with the help of special software. The computer can then simulate three-dimensional temperature distribution in the mold. If undesirable temperature values occur in certain areas, the previously defined temperature channel layout can be changed. Through the simulation, the temperature control system can be virtually changed until a possibly optimum condition is achieved. The advantage of this technique is that the simulation allows a three-dimensional view of the heat flows and temperatures. In addition, this technique is very accurate (but only if the boundary conditions have been practically defined ). The disadvantages are the costs and the need for specialized staff and appropriate software licenses. Therefore, such designs are often purchased as a service. 

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