Accurate discretization of gradients on non-uniform curvilinear staggered grids

It is shown how to discretize the pressure gradient in the Navier-- Stokes equations on an arbitrary non-uniform curvilinear staggered grid, such that the error is zero for constant pressure gradient. A theoretical foundation is given for a discretization proposed in [2] on empirical grounds. A quite similar approach is used to discretize a diffusion equation with strongly discontinuous diffusion coefficient, such that the error is zero on a general grid for constant flux. 1 Introduction Keeping only the pressure term, the equations of incompressible flow are given by the following reduced form of the Navier--Stokes equations: @u=@t +rp = 0 (1.1) divu = 0 (1.2) with r the gradient operator. The following equation \Gamma div(Drp) = oe (1.3) plays an important role in the theory of flow in porous media, and closely resembles the pressure equation in the IMPES (implicit pressure, explicit saturation) model in reservoir engineering. Often the domain contains interfaces across which D ha..

INTRINSIC VASODILATION PROTECTS WISTAR KYOTO RATS FROM PROGRESSIVE GLOMERULOSCLEROSIS AFTER UNILATERAL NEPHRECTOMY

Genetically determined differences in functional and structural determinants that govern the development of progressive glomerulosclerosis (GS) were studied in aging sham-operated or unilaterally nephrectomized male rats of two strains. Wistar rats showed an increase of proteinuria and GS with age, which was enhanced by unilateral nephrectomy (UN). In contrast, intact and UN Wistar Kyoto rats did not show an increase of proteinuria with age and 7 months after UN, no GS was seen in these rats. Systemic blood pressure was comparable in both strains and was not affected by UN. Functional studies in a separate group of rats 1 month after UN showed an identical increase in glomerular filtration rate in both strains as compared with sham-operated controls. The Wistar rats did not show an effect of UN on renal plasma flow, and consequently, there was an increase in filtration fraction, in contrast to Wistar Kyoto rats, which showed an increase in renal plasma flow with an unchanged filtration fraction. Glomerular volume was increased in both strains at 1 month and 7 months after UN. Mesangial expansion was not observed at 1 month after UN in either strain, which indicates that this is not a decisive factor in the development of GS. These data indicate that the genetically determined susceptibility to the development of GS in these two rat strains may be related to the degree of vasoconstriction, whereas glomerular volume expansion per se does not lead to GS but can well be a consequence of hyperfiltration. These studies are concordant with previous studies that revealed the role of hemodynamics in the pathogenesis of GS irrespective of glomerular expansion

Parallelism in GMRES applied to the computation of incompressible flows

the computation of incompressibl

Some parallelizable preconditioners for GMRES

Some preconditioners that show potential for parallelization are examined to judge their efficiency relative to the current ISNaS incompressible flow solver preconditioners. The experiments show that in 2D parallel versions of the current preconditioners outperform there rivals. In 3D the approximate inverse preconditioner shows promise as preconditioner for the pressure equation