n i v e r s i t yo fN o t r eD a m e ,I N4 6 5 5 6 ,U S A SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

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SUMMARYA new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601×601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.

SUMMARYThe widely studied benchmark problem, 2-D driven cavity flow problem is discussed in details in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. Based on the several numerical and experimental studies, the fact of the matter is, above moderate Reynolds numbers physically the flow in a driven cavity is not twodimensional. However there exist numerical solutions for 2-D driven cavity flow at high Reynolds numbers.

Numerical solutions of 2-D steady incompressible flow inside a triangular cavity are presented. For the purpose of comparing our results with several different triangular cavity studies with different triangle geometries, a general triangle mapped onto a computational domain is considered. The Navier-Stokes equations in general curvilinear coordinates in streamfunction and vorticity formulation are numerically solved. Using a very fine grid mesh, the triangular cavity flow is solved for high Reynolds numbers. The results are compared with the numerical solutions found in the literature and also with analytical solutions as well. Detailed results are presented.

The benchmark test case for non-orthogonal grid mesh, the "driven skewed cavity flow", first introduced by Demirdžiü et al. [5] for skew angles of

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

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