By H. Oh
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076 L and solve the Euler equations with the CABARET method. For this calculation, the computational grid with the resolution of 7-8 cells per acoustic wavelength that corresponds to (1000x1200) grid cell points is used. s. field obtained from the Euler solution, where the loci of the caustics bifurcating into two branches, as obtained in Colonius at al (1994), are shown. The centre of the vortex corresponds to the origin of the coordinate system. The caustics branches outline the acoustic interference zone that develops behind the vortex.
The results for two pseudo-spectral optimised dispersion schemes are also shown. Note that the dispersion errors of semi-discrete schemes correspond to exact integration in time, which neglects the possible increase of dispersion error due to inaccuracies in time marching. For most Courant numbers and for a wide range of grid resolution (7-20 points per wavelength) the dispersion error of the CABARET scheme remains below that of the conventional and optimised fourth-order central finite differences and close to that of the six-order central schemes.
204. To simplify the treatment of external boundary conditions, the box size is set 20 times as large as the vortex radius, L so that the vortex induced velocity vanishes at the boundaries. , Colonius at al, 1994). The characteristic space scale of the problem is the vortex core radius L. 047 . 25 Direct Numerical Simulations of Compressible Vortex Flow Problems The analytical solution of the problem is trivial: at all time moments the solution remains equal to the initial conditions. From the viewpoint of unsteady computational schemes, however, preserving the vortex solution on a fixed Eulerian grid that is not specifically tailored to the initial vortex shape tends to be a challenge.
Advanced Fluid Dynamics by H. Oh