In this research we have implemented the Random vortex Method to calculate velocity fields of fluids inside open cavities in both turbulent and laminar flows. the Random vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map the physical geometry into the upper half plane. In some complex geometries like the flow inside cavity, the Schwarz-Christoffel mapping which transfers the cavity into the upper half plane cannot be achieved easily. In this paper, the mentioned mapping function for a square cavity is obtained numerically. Then, the instantaneous and the average velocity fields are calculated inside the cavity using the RVM. Reynolds numbers for laminar and turbulent flows are 50 and 50000, respectively. In both cases, the velocity distribution of the model is compared with the FLUENT results that the results are very satisfactory. Also, for aspect ratio the cavity (α ) equal 2, the same calculation was done for Re=50 and 50000. The advantage of this modelling is that for calculation of velocity at any point of the geometry, there is no need to use meshing in all of the flow field and the velocity in a special point can be obtained directly and with no need to the other points.

This research describes unsteady two-dimensional reacting flow around a circular cylinder. The numerical solution combines Random vortex method for incompressible two dimensional viscous fluid flow with a Simple Line Interface Calculation (SLIC) algorithm for propagation of flame interface. To simplify the governing equations, two fundamental assumptions namely Low Mach Number and Thin Flame Thickness are used. Numerical and graphical representation of vorticity field, velocity variation on the wake axis, the effect of combustion on stream line pattern and location of vortex element at Reynolds numbers of 3000 and 9500 are discussed. The numerical results for the non-reacting flows fall within the range of the experimental measurements while the results of the reacting case are qualitatively following the physics.

Direct numerical simulation of the wake flow around and behind a planar ellipse using a Random vortex method is presented. Fluid is considered incompressible and the aspect ratios of ellipse and the angles of attacks are varied. This geometry can be a logical prelude to the more complex geometries, but less time dependent experimental measurements are available to validate the numerical results. Therefore, the key figures of the averaged values of selected cases are chosen to check the accuracy of the results. Based on the results, the general behavior of the flow around an ellipse at the zero angle of attack is almost similar to that around a circle. But, at the other angle of attacks, the asymmetry of the flow is dominant and pronounced clearly.

In this paper the turbulent, incompressible and unsteady viscous flow around a circular cylinder is numerically simulated and the imposed fluid forces are calculated. The Random vortex Method (RVM) with the using of a Large-Eddy Simulation (LES), as a turbulence modelling, is developed to investigate the fluid flow around a circular cylinder. A LES of turbulent flow is applied to account for the effect of turbulence in the wake. The Navier-Stokes equations are filtered by LES and transformed to computational domain by a general conformal transformation. The fil- tered equations are solved by an operator splitting where the velocity is found from Cloud-in-Cell (CIC) method and the diffusion equation is modeled by Random walks (RW). The numerical results lift, darg coefficients and Strouhal number are in reasonable agreement with experimental results.

In this paper, numerical simulation for a two-dimensional viscous and incompressible flow past the elliptical airfoil is presented by Random vortex Blob (RVB). RVB is a numerical technique to solve the incompressible, two-dimensional and unsteady Navier-Stocks equations by converting them to rotational non-primitive formulations. In this method, the velocity vector at a certain point can be calculated without considering any grid around it, so the RVB method can be treated as a meshless method. Accordingly, the turbulent flow past a cylinder as well as an elliptical airfoil is investigated. In both cases, the obtained mean time velocities are compared with available numerical and experimental results where an acceptable agreement is observed. Having known the velocity field, by employing momentum balance, the drag and lift coefficients caused by flow past the elliptical airfoil with different diameter ratios and Re=105 are calculated and compared with experimental data where a good consistency is achieved.

Direct numerical simulation of turbulent flow behind a cylinder, wake flow, using the Random vortex method for an incompressible fluid in two dimensions is presented. In the Random vortex method, the primary variable is vorticity of the flow field. After generation on the cylinder wall, it is followed in two fractional time step in a Lagrangian system of coordinates, namely convection and diffusion. No closure model is used and the instantaneous results are calculated without any a priori modeling. Regarding the Lagrangian nature of the method, there is a very good compatibility between the numerical method and physics of the flow. The numerical results are presented for a wide range of Reynolds number, 40-9500. In the initial stages, there is only an unstable symmetrical flow behind the cylinder and the vortex shedding is not started yet. But, in the high Reynolds number flows, two distinctive flow patterns, namely a and b are detected. The mechanism of generation of the primary and the secondary eddies can be related to the production, convection and diffusion of the vorticity field and the time dependent structure of the flow field in the wake zone behind the cylinder. The length of the computational domain, downstream of the cylinder, is selected 25 times of the cylinder's diameter. Regarding such a lengthy computational domain it is possible to detect the mechanism of generation, pairing and growth of the large scale structure, eddies. Although the instantaneous numerical results are calculated, no coresponding comparable results are available. Therefore, the validity of the results in this stage is only qualitative. For the quantitative comparison of the results, after the establishment of the stationary state, time averaged based indicators such as separation angle, drag coefficient, lift coefficient, Strophe umber and ... are calculated. The numerical results accurately fall within the range of the experimental measurements.