A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Cyclooxygenase-2 mediates the cardioprotective effects of the late phase of ischemic preconditioning in conscious rabbits

We examined the role of cyclooxygenase-2 (COX-2) in the late phase of ischemic preconditioning (PC). A total of 176 conscious rabbits were used. Ischemic PC (six cycles of 4-min coronary occlusions/4-min reperfusions) resulted in a rapid increase in myocardial COX-2 mRNA levels (+231 ± 64% at 1 h; RNase protection assay) followed 24 h later by an increase in COX-2 protein expression (+216 ± 79%; Western blotting) and in the myocardial content of prostaglandin (PG)E2 and 6-keto-PGF1α (+250 ± 85% and +259 ± 107%, respectively; enzyme immunoassay). Administration of two unrelated COX-2 selective inhibitors (NS-398 and celecoxib) 24 h after ischemic PC abolished the ischemic PC-induced increase in tissue levels of PGE2 and 6-keto-PGF1α. The same doses of NS-398 and celecoxib, given 24 h after ischemic PC, completely blocked the cardioprotective effects of late PC against both myocardial stunning and myocardial infarction, indicating that COX-2 activity is necessary for this phenomenon to occur. Neither NS-398 nor celecoxib lowered PGE2 or 6-keto-PGF1α levels in the nonischemic region of preconditioned rabbits, indicating that constitutive COX-1 activity was unaffected. Taken together, these results demonstrate that, in conscious rabbits, up-regulation of COX-2 plays an essential role in the cardioprotection afforded by the late phase of ischemic PC. Therefore, this study identifies COX-2 as a cardioprotective protein. The analysis of arachidonic acid metabolites strongly points to PGE2 and/or PGI2 as the likely effectors of COX-2-dependent protection. The recognition that COX-2 mediates the antistunning and antiinfarct effects of late PC impels a reassessment of current views regarding this enzyme, which is generally regarded as detrimental.