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Two methods for a faster convergence of numerical simulation of steady state problems in soft wall and outer boundary conditions were developed to examine the behavior of residual waves. These solutions were tested in one- and two-dimensional applications. Results show that the acoustic waves affect the convergence process and the acoustic behavior is almost totally dominant when correlating the pressure and density residuals.

The problem of the optimum shape for tin cans depends upon the volume of the cans, as shown by a calculus model. The resulting optimal shape approaches a square for large sizes and is tall and thin for small volumes. An asymptotic curve can be graphed for the relation of volume to cubic length of material which can be joined for the cost per unit area.

In numerical solutions of fluid flow, vorticity can be generated by truncation errors. We analyze this phenomenon for linearized equations and give conditions for preventing it. The Lax Wendroff method that meets these constraints is essentially unique, although there are two distinct interpretations, and also turns out to have optimal properties regarding stability and truncation error. The extension of the scheme to unstructured grids is given, together with some discussion of practical problems to which these schemes might bring improvement. [ABSTRACT FROM AUTHOR]