Vortex Dynamics Studied by Large-Scale Solutions to the Euler Equations
Numerical solutions to the Euler equations have been found to exhibit the realistic behaviour of some vortex flows, but the fundamental question surrounding these is the way by which the vorticity initially is created in the flow. One explanation lies in the nonlinear occurrence of vortex sheets admitted as a solution to the Euler equations. The sheets may arise from the build up and breaking of simple shear waves, and seems associated with singular points of the surface velocity field where the flow separates from the body. In order to gain insight into this situation a numerical method to solve either the compressible or incompressible Euler equation in three dimensions is described. The computational procedure is of finite-volume type and highly vectorized, achieving a rate of 125 M flops on the CYBER 205, and allows the use of very dense meshes necessary to resolve the local features like the singular points. Several flow problems designed to test the vortex-sheet hypothesis are solved upon a mesh with over 600,000 grid cells. These solutions, even when the body is smooth, present numerical observations of such vortex sheets and singular points which support the hypothesis. One such computation runs in about 2 hours of CPU time on the CYBER 205 supercomputer.
KeywordsSingular Point Euler Equation Truncation Error Vortex Sheet Delta Wing
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