Shuvam Sen

α-, β-phenomena in the post-symmetry break for the flow past a circular cylinder

In the existing literature, the so-called α- and β-phenomena have been reported only for the early stages for the flow past an impulsively started circular cylinder. The current study endeavours to explore the possible existence of these phenomena even in the later stages of the flow. The flow is computed using a recently developed compact finite difference method for the biharmonic form of the two-dimensional Navier-Stokes equations for a wide range of Reynolds numbers (Re). We establish that these secondary phenomena not only appear once the wake becomes asymmetric but also periodically during the post-vortex shedding period for Re = 1000. Further, the recently reported sub-α- and sub-β-phenomena for Re = 5000 at the tertiary level during the early stages of the flow could be identified even during the later stages of the flow as well. The formation of these tertiary structures has been explained through a detailed theoretical characterization of the topological aspects of the boundary layer separation....

A 4OEC scheme for the biharmonic steady Navier–Stokes equations in non-rectangular domains

Abstract Recently the biharmonic form of the Navier–Stokes (N–S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N–S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation that were developed for Cartesian coordinate system, this scheme is capable of numerically solving the two-dimensional N–S equations using body fitted coordinate system. Despite the presence of extra derivative terms in the quasi-linear form of the biharmonic equation, our extended formulation continues to maintain its fourth order accuracy on a nine-point compact stencil. A spectral analysis on the scheme reveals its superior resolution properties. The formulation has been tested on fluid flow problems of varied complexities on different geometries which includes flow past an impulsively started circular cylinder and elliptic aerofoil with angles of attack. We present our numerical results and validate them with established numerical and experimental observations available in the literature; excellent comparison is obtained in all the cases.

On the Development of a Nonprimitive Navier---Stokes Formulation Subject to Rigorous Implementation of a New Vorticity Integral Condition

In this paper, a new integral vorticity boundary condition has been developed and implemented to compute solution of nonprimitive Navier–Stokes equation. Global integral vorticity condition which is of primitive character can be considered to be of entirely different kind compared to other vorticity conditions that are used for computation in literature. The procedure realized as explicit boundary vorticity conditions imitates the original integral equation. The main purpose of this paper is to design an algorithm which is easy to implement and versatile. This algorithm based on the new vorticity integral condition captures accurate vorticity distribution on the boundary of computational flow field and can be used for both wall bounded flows as well as flows in open domain. The approach has been arrived at without utilizing any ghost grid point outside of the computational domain. Convergence analysis of this alternative vorticity integral condition in combination with semi-discrete centered difference approximation of linear Stokes equation has been carried out. We have also computed correct pressure field near the wall, for both attached and separated boundary layer flows, by using streamfunction and vorticity field variables. The competency of the proposed boundary methodology vis-a-vis other popular vorticity boundary conditions has been amply appraised by its use in a model problem that embodies the essential features of the incompressibility and viscosity. Subsequently the proposed methodology has been further validated by computing analytical solution of steady Stokes equation. Finally, it has been applied to three benchmark problems governed by the incompressible Navier–Stokes equations, viz. lid driven cavity, backward facing step and flow past a circular cylinder. The results obtained are in excellent agreement with computational and experimental results available in literature, thereby establishing efficiency and accuracy of the proposed algorithm. We were able to accurately predict both vorticity and pressure fields.

Tackling Problems of Moving Boundaries Using the Biharmonic Approach

In this paper, we apply the biharmonic pure stream function form of the Navier-Stokes equations to study flow problems symbolizing moving boundaries. A newly developed second-order temporally and spatially accurate finite difference scheme for transient biharmonic semi-linear equations has been used to simulate flow past a cylinder with constant and oscillatory rotation. The main focus here is the application of the technique, which enables the use of the discretized version of a single semi-linear biharmonic equation in order to efficiently simulate flows around a bluff body with moving boundaries. We compare our results, both qualitatively and quantitatively, with established numerical and more so, with experimental results. Excellent comparison is obtained in all of the cases.