Rajendra K. Ray

A transformation-free HOC scheme for incompressible viscous flows past an impulsively started circular cylinder

In this paper, we present a higher order compact scheme for the unsteady two-dimensional (2D) Navier-Stokes equations on nonuniform polar grids specifically designed for the incompressible viscous flows past a circular cylinder. The scheme is second order accurate in time and at least third order accurate in space. The scheme very efficiently computes both unsteady and time-marching steady-state flow for a wide range of Reynolds numbers ( Re ) ranging from 10 to 9500 for the impulsively started cylinder. The robustness of the scheme is highlighted when it accurately captures the vortex shedding for moderate Re represented by the von Karman street and the so called α and s -phenomena for higher Re. Comparisons are made with established numerical and experimental results and excellent agreement is found in all the cases, both qualitatively and quantitatively.

Iterative solvers for image denoising with diffusion models: A comparative study

Abstract In this paper we propose and compare the use of two iterative solvers using the Crank–Nicolson finite difference method, to address the task of image denoising via partial differential equations (PDEs) models such as Regularized Perona–Malik equation or C -model and Bazan model (Bilateral-filter-based model). The solvers which are considered in this paper are the Successive-over-Relaxation (SOR) and an advanced solver known as Hybrid Bi-Conjugate Gradient Stabilized (Hybrid BiCGStab) method. From numerical experiments, it is found that the Crank–Nicolson method with hybrid BiCGStab iterative solver produces better results and is more efficient than SOR and already existing, in terms of MSSIM and PSNR.

A Transformation-free HOC Scheme for Incompressible Viscous Flow Past a Rotating and Translating Circular Cylinder

In the present work, a numerical study is made using a recently developed Higher Order Compact (HOC) finite difference scheme to test its capacity in capturing the very complex flow phenomenon of unsteady flow past a rotating and translating circular cylinder. The streamfunction-vorticity formulation of the Navier-stokes equations in cylindrical polar coordinate are considered as the governing equations. In the present investigation, flow is computed for a fixed Reynolds number (Re) 200 and rotational parameter values 0.5, 1.0, 2.07 and 3.25 are considered. Firstly, the flow patterns for different α values and for long time range are computed and qualitative comparisons are made with existing experimental and numerical results. Then, as a further check on the consistency of the experimental and present numerical results, quantitative comparisons are made for the velocity profiles at several locations. All these qualitative and quantitative comparisons show excellent agreements with existing experimental and numerical results.

Stability Analysis of an Integro Differential Equation Model of Ring Neural Network with Delay

In this paper we present and study a ring neural network model with delays. We study existence and uniqueness of equilibrium point and global stability of the model system. At the end few examples have been given to illustrate the analytical findings.

Numerical Simulation of Flow Around Square Cylinder with an Inlet Shear in a Closed Channel

In this paper, two-dimensional unsteady flow of incompressible fluid past a square cylinder placed in a closed finite domain is studied in the presence of an inlet linear shear velocity profile. The flow has been investigated for Reynolds number \(Re = 100\) and shear rate \(K = 0.0, 0.05, 0.1\). The governing equations are solved by using the higher order compact (HOC) finite difference scheme. The purpose of the present study is to elaborate the influence of shear rate on the vortex shedding phenomenon behind the square cylinder. The results are presented in terms of streamline pattern, vorticity contours, lift–drag coefficients, and their corresponding power spectra. It is observed that the vortex shedding phenomenon strongly depends on \(Re\) as well as \(K\). The strength and size of vortices vary as a function of \(Re\) and \(K\), but not significantly for the current values of parameters.

A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme

The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in αm on the timing of the formation of the vortices, the closed wake length, and the thickness of the boundary layer is investigated.The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and v...

Higher Order Compact Numerical Simulation of Shear Flow Past Inclined Square Cylinder

The numerical simulation of 2D unsteady, incompressible shear flow past square cylinder with an angle of incidence (α = 45°) is carried out in this paper. Simulations are performed using ψ-ω formulation of Navier-Stokes equations on compact uniform grid. Higher Order Compact (HOC) formulation is used to discretize the governing equations. Numerical results are presented for Reynolds number Re = 100 with three different shear parameters K = 0.0, 0.05 and 0.1. Computed results are compared with existing numerical results. Our computed results are found to produce better approximation of the exact flow dynamics. Shedding frequency is seen to decrease with increasing K.

A Cartesian Grid Method for Solving Stokes Equations with Discontinuous Viscosity and Singular Sources

In this paper, we present a new finite difference scheme for solving incompressible, steady stokes equations in discontinuous domains. While solving two phase Stokes equations, across some interfaces, there are discontinuities in the pressure, viscosity and velocity. Since, these jump conditions are coupled together, it is difficult to discretise and solve the system of equations accurately. We apply the augmented approach introduced by Li et al. (Int J Numer Meth. Fluids 44:33–53, 2004) to decouple these jump conditions. A new finite difference method is then developed and presented to solve the resulting augmented system of Stokes equations. Points of intersection of grid lines and the interface are used as a node in the finite difference stencil and jump conditions are then used to determine the values at these intersection points. Numerical solutions are compared with the corresponding analytical solutions and those of the augmented immersed interface method. The method is found to be second order accurate for almost all the variables in the infinity norm.

A Comparative Study of Iterative Solvers for Image De-noising

In this paper we propose and compare the use of two iterative solvers using the Crank-Nicolson finite difference method, for image denoising via Partial differential equations (PDE) models such as Bilateral-filter-based model. The solvers considered here are: Successive-over-Relaxation (SOR) and an advanced solver known as Hybrid Bi-Conjugate Gradient Stabilized (Hybrid BiCGStab) method. We demonstrate that proposed hybrid BiCGStab solver for denoising yields better performance in terms of MSSIM and PSNR, and is more efficient than existing SOR solver and a state-of-the-art approach.

A Transform Free Higher Order Compact Finite Difference Scheme for Simulating the Flow behind a Rotationally Oscillating Circular Cylinder at Reynolds Number 500

Two-dimensional incompressible, viscous fluid flow around a rotationally oscillating circular cylinder is studied numerically by using a recently developed higher order compact finite difference scheme (HOC) at Reynolds number Re = 500. The stream function vorticity formulation of Navier Stokes equations in cylindrical polar coordinates are considered as the governing equations. Different values of peak rotation rate αm and forced oscillation frequency fe are considered. The simulated results are in a good agreement both qualitatively and quantitatively with the previously published results.