Test Problems, Coordinate Transformations, and Technique for Nonsteady Compressible Flow Analysis,
NAVAL SURFACE WEAPONS CENTER DAHLGREN VA
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This paper describes a finite difference technique for solving problems in nonsteady, two-dimensional, inviscid flow of an ideal gas. The technique solves the equations of gas dynamics in transformed coordinates obtained by conformal mapping of the physical domain of the problem. Irregular physical domains with curved or piecewise-straight boundaries are transformed onto rectangles to facilitate the application of boundary conditions in the finite difference calculations. The differential equations fo fluid flow in conservation law form are solved by means of either the two-step Lax-Wendroff of MacCormacks finite difference method. An expedient means of obtaining coordinate transformations by a numerical integration of a Schwartz-Christoffel type differential equation has been used for problems in transient external aerodynamics. An extensive series of test problems, consisting of one-dimensional traveling shock waves, two-dimensional steady Prandtl-Meyer expansions, and oblique shocks were solved so that the finite difference calculations could be compared with exact mathematical results. Nonsteady Mach reflections were computed and compared with approximate theory and experimental data to test the technique for problems that are both fully two-dimensional and nonsteady.