Hexahedral grid

A hexahedral grid is the optimum solution. Commercial grid codes tend to fail in the complex intermeshing area between the two screws. 

Coordinate origin was fixed at the lower left corner of refuge chamber s model. People-models were toward positive direction of X-axis. Then the models were divided with total 800000 hexahedral grids, as shown in Fig. 2. Adopted dividing principles are as follows ... 

Highly skewed cells should be avoided. The angles between the grid lines of a hexahedral mesh should be 90°. Angles < 40° or > 140° often imply a reduced accuracy or numerical instabilities. 

Perhaps the most traditional way to solve Equation 23.1 utilizes the FD approach by discretizing the solution domain S2 using a grid of uniform hexahedral elements. The coordinates of a typical grid point are x = lh,y = mh, z = nh (/, m,n = integers), and the value of (x,y,z) at a grid point is denoted by Taylor s theorem can then be utilized to provide the difference equations. For example ... 

Numerical implementation of the boundary conditions is conducted by the use of the IN-FORM tool in PHOENICS 2008, which increases the simulation time, as higher computational effort is demanded. On the other hand, it represents a simpler and more intuitive manner of dealing with complex initial or boundary conditions. A point-history object is used to track the plume concentration reached on a location at a distance of about 750 meters far from the source point. A lighter-than-air gas is considered and a single density calculation is conducted for the whole domain, as a fimction of the gas fraction (mixture air and gas). A monitoring time of 30 minutes is simulated by the use of adequate time and space grids 9000 time steps (0.2 s for each) and about 18,000 hexahedral cells. 

A number of commercially available computational fluid dynamics (CFD) models could be used for the prediction of squat. At the core of any CFD problem is a computational grid or mesh where the solution is divided into thousands of elements. These elements are usually 2D quadrilaterals or triangles and three-dimensional (3D) hexahedral, tetrahedral, or prisms. Mathematical equations are solved for each element by the numerical model. For hydrodynamics the Navier-Stokes equations (NSEs) can be solved to include viscosity and turbulence. The NSEs provide detailed prediction (vortices) of the flow field, but require very thin meshes, high central processing unit (CPU) time, and memory storage. Its resolution is also quite difficult with numerical instabilities. Examples of commercial CFD models include Fluent and Fidap. 

In laminar flows, the grid near boundaries should be refined to allow the solution to capture the boundary layer flow detail. A boundary layer grid should contain quadrilateral elements in 2D and hexahedral or prism elements in 3D, and should have at least five layers of cells. For turbulent flows, it is customary to use a wall function in the near-waU regions. This is due to the fact that the transport equation for the eddy dissipation has a singularity at the wall, where k [in the denominator in the source terms in eq. (5-14)] is zero. Thus, the equation for e must be treated in an alternative manner. Wall functions rely on the fact... 

Figure 5-5 (a) Unstructured grid using hexahedral elements, (b) Unstructured grid using... 

The initial mesh consists of uniform hexahedral cells. Mesh dependency tests have been performed, which exhibit that the simulation results are reasonably grid independent when the cube width (a) is resolved by at least ten cells. The left of Fig. 18.44 exhibits the variation of the particle velocity during penetration while the right displays the temporal evolution of the penetration process. For the rough mesh resolution (a/A = 5), the simulation collapsed at the moment of 5 ps. 

A grid is a decomposition of some volume, 1 , into a finite set of subvolumes, such that (i) the union of the subvolumes is approximately equal to the parent volume and (ii) most of the intersection of the surfaces of any pair of subvolumes is included in the intersection of their respective volumes. The subvolumes are called cells or blocks. Thus one is allowing some finite volume of overlap between subvolumes and also some holes provided that the offending volumes are small. Ideally the volume of overlap and of holes will be zero, but in complicated geometries and with the possible constraint to hexahedral cells this is not always practical. 

Flows in 2D or 3D geometries using unstructured solution-adaptive triangular/tetrahedral, quadrilateral/hexahedral, or mixed (hybrid) grids that include prisms (wedges) or pyramids (Both conformal and hanging-node meshes are acceptable.) ... 

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