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Incompressible and Anelastic Flow Simulations on Numerically Generated Grids

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  • 1 Department of Atmospheric Sciences, University of California, Los Angeles, California
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Abstract

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property or orthogonality has been preserved. Flow equations in general curvilinear coordinate maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible modern using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Abstract

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property or orthogonality has been preserved. Flow equations in general curvilinear coordinate maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible modern using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

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