the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

We present a fourth order compact nite diierence scheme on the face centered cubic (FCC) grids for the numerical solution of the two dimensional convection diiusion equation. The seven point formula is deened on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, eecient, and concise. A corresponding multigrid method is d...

A technique for directly probing CP violation in the Higgs sector of a multidoublet model using gluon-gluon collisions at the SSC is reviewed.

I review new developments in Higgs physics and electroweak symmetry breaking that have resulted from the Madison–Argonne workshops on SSC physics.

The simplest finite difference approximations for spatial derivatives are centered, explicit, and applied to “regular” equispaced grids. Well-established generalizations include the use of implicit (compact) approximations and staggered grids. We find here that the combination of these two concepts, together with high formal order of accuracy, is very effective for approximating the first deriv...

Finite-volume discretization schemes for viscous fluxes on general grids are compared using node-centered and cell-centered approaches. The grids range from regular grids to highly irregular grids, including random perturbations of the grid nodes. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes (a node-...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...