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NUMERICAL INTEGRATION EXPERIMENTS WITH VARIABLE-RESOLUTION TWO-DIMENSIONAL CARTESIAN GRIDS USING THE BOX METHOD

WALTER JAMES KOSSNational Hurricane Research Laboratory, Environmental Research Laboratories, NOAA, Miami, Fla.

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Abstract

Numerical experiments were performed with variable resolution two-dimensional rectangular Cartesian grids. The shallow-water equations were integrated on several variable-mesh grids and on a constant increment fine-resolution grid; the method of integration used the “box” technique for spatial representation. The grids were designed to be used in numerical experiments that examine vortex-type motions that may be embedded in a fairly uniform basic current. With this in mind, two systems were investigated: (1) a closed system containing a balanced vortex and (2) a semiopen system with east-west cyclic continuity containing a moderately strong easterly jet. The results indicate that, for a weak vortex embedded in a zonal current, a 2-step “telescope”-type grid can be used in numerical integrations with success; that is, the incurred error is relatively small and the computation time and computer memory requirements are not excessive. For an intense vortex, a graded-type grid yields a relatively better numerical integration at the expense of an increase in computation time.

Abstract

Numerical experiments were performed with variable resolution two-dimensional rectangular Cartesian grids. The shallow-water equations were integrated on several variable-mesh grids and on a constant increment fine-resolution grid; the method of integration used the “box” technique for spatial representation. The grids were designed to be used in numerical experiments that examine vortex-type motions that may be embedded in a fairly uniform basic current. With this in mind, two systems were investigated: (1) a closed system containing a balanced vortex and (2) a semiopen system with east-west cyclic continuity containing a moderately strong easterly jet. The results indicate that, for a weak vortex embedded in a zonal current, a 2-step “telescope”-type grid can be used in numerical integrations with success; that is, the incurred error is relatively small and the computation time and computer memory requirements are not excessive. For an intense vortex, a graded-type grid yields a relatively better numerical integration at the expense of an increase in computation time.

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