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High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.

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The aim of this study was to investigate the feasibility of a quantitative structure-pharmacokinetic relationships (QSPKR) method based on contemporary three-dimensional (3D) molecular characterization and multivariate statistical analysis. For this purpose, the programs SYBYL/CoMFA, GRID, and Pallas, in combination with the multivariate statistical technique principal component analysis were employed to generate a total of 16 descriptor variables for a series of 12 structurally related adenosine A1 receptor agonists. Subsequently, the multivariate regression method, partial least squares, was used to predict clearance (CL), volume of distribution (VdSS) and protein binding (fraction unbound, fU). The QSPKR models obtained could account for most of the variation in CL, VdSS, and fU (R2 = 0.82, 0.61 and 0.78, respectively). Cross-validation confirmed the predictive ability of the models (Q2 = 0.59, 0.41 and 0.62 for CL, VdSS, and fU, respectively). In conclusion, we have developed a multivariate 3D QSPKR model that could adequately predict overall pharmacokinetic behavior of adenosine A1 receptor agonists in rat. This methodology can also be used for other classes of compounds and may facilitate the further integration of QSPKR in drug discovery and preclinical development.

SUMMARYWe have introduced multilinear PLS in 3D QSAR and applied it to GRID descriptors from a set of benzamides with affinity to the dopamine D 3 receptor subtype, synthesized as potential drugs against schizophrenia. The key issue in 3D QSAR modelling is to obtain a predictive model that is easy to interpret. Each component in the multilinear PLS model explains clearly defined details, e.g. substituent positions, while the bilinear PLS solution is general and more difficult to interpret. The best models were obtained after four components with multilinear PLS (Q 2 = 51%) and after only one component with bilinear PLS (Q 2 = 50%). The external test set was predicted better with multilinear PLS (Q 2 = 31%) than with bilinear PLS (Q 2 = 25%). With multilinear PLS one loses in fit and gains in stability and simplicity owing to the fewer parameters that need to be estimated as compared with bilinear PLS. Finally, multilinear PLS is also less influenced by insignificant variation in the descriptor block, which is an advantage in 3D QSAR modelling

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