By H. Oh
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In the present subsection, the problem of counter-rotating vortices is solved on a fixed Eulerian grid for the range of Reynolds numbers, Re=5000-10000 with the conservative Navier-Stokes CABARET method. Fig. 8 shows the problem setup. Four viscous-core counter-rotating vortices are initiated in an open domain. 3 and x y 103 r0 is half-distance between the adjacent vortex centres. 2 . The initial location of the centre of mass of the system corresponds to x=0. 32 Advanced Fluid Dynamics 2 2 Fig.
345-416. M. : The contour-advective semiLagrangian algorithm for the shallow water equations. Mon. Wea. Rev. 127(7), pp. 1551–1565 (1999). , “The dynamics and acoustics of viscous two-dimensional leapfrogging vortices”, J. , 301 (2007) 74–92. Fritsch G. , “Second-order effects of unsteadiness on the performance of turbomachines”, ASME Paper 92-GT-389; 1992. M. Soc. of America, Vol. 51, No. 1 (Part 2) pp. 206-209 (1972). M. A. “Difference approximation of convective transport with spatial splitting of time derivative”, Mathematical Modelling, Vol.
By construction, such methods are particularly efficient in handling linear wave phenomena. The optimized finite-difference methods were developed to overcome typical problems of spectral and pseudo-spectral methods by handling non-periodic boundary conditions and large flow gradients which they handle with the use of hyper diffusion. On the other hand, there is another popular approach, based on the conservation properties of the governing equations, that forms the basis for the so-called shock-capturing schemes.
Advanced Fluid Dynamics by H. Oh