Orthogonal grid

Besides the aforementioned descriptors, grid-based methods are frequently used in the field of QSAR quantitative structure-activity relationships) [50]. A molecule is placed in a box and for an orthogonal grid of points the interaction energy values between this molecule and another small molecule, such as water, are calculated. The grid map thus obtained characterizes the molecular shape, charge distribution, and hydrophobicity. 

Besides the convective fluxes, the diffusive fluxes on the control volume faces have to be determined. As apparent from Eq. (33), an expression for dO/dsc containing the nodal values of O is needed. In the case of an orthogonal grid aligned with the axes of a Cartesian coordinate frame, the expression... 

The spatial-transport algorithm is relatively easy to implement on orthogonal grids using information provided by the FV code. 

The effective flow rates are grid-dependent and relatively difficult to compute for arbitrary non-orthogonal grids. 

Relative to Eulerian PDF codes, particle tracking and sorting on non-orthogonal grids is computationally intensive, and can represent a large fraction of the total computational cost. 

The PDF codes presented in this chapter can be (and have been) extended to include additional random variables. The most obvious extensions are to include the turbulence frequency, the scalar dissipation rate, or velocity acceleration. However, transported PDF methods can also be applied to treat multi-phase flows such as gas-solid turbulent transport. Regardless of the flow under consideration, the numerical issues involved in the accurate treatment of particle convection and coupling with the FV code are essentially identical to those outlined in this chapter. For non-orthogonal grids, the accurate implementation of the particle-convection algorithm is even more critical in determining the success of the PDF simulation. 

There are many programs which can be used compute the electrostatic potential around a molecule. A computer model is first prepared from the x, y, z coordinates of the atoms, and this model is then surrounded by an imaginary orthogonal grid. 

FIGURE 7.21 A typical control volume (2D) for non-orthogonal grid. 

Apart from the convective and diffusive fluxes, it is also necessary to evaluate source terms. As mentioned in the previous chapter, the volume integral can be calculated as a product of the CV center value of the integrand and the CV volume. This approximation is independent of the CV shape. For non-orthogonal grids, the calculation of the cell volume becomes more complicated. For 2D quadrilaterals, the... 

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