Sanyasiraju VSS Yedida

In this study free vibrations of anti-symmetric angle-ply composite plates including shear deformation under clamped-clamped boundary conditions are presented. Two types of numerical methods are adopted to analyze the problem. The spline and radial basis functions base mesh free scheme are applied simultaneously to approximate the displacement and rotational functions. Comparative studies have been made for analyzing the frequency parameters with respect to the material properties, number of layers, fiber orientations, side-to-thickness ratio and aspect ratio. The results are depicted in terms of tables and graphs.

In this paper, two radial basis function (RBF)-based local grid-free upwind schemes have been discussed for convection-diffusion equations. The schemes have been validated over some convection-diffusion problems with sharp boundary layers. It is found that one of the upwind schemes realizes the boundary layers more accurately than the rest. Comparisons with the analytical solutions demonstrate that the local RBF grid-free upwind schemes based on the exact velocity direction are stable and produce accurate results on domains discretized even with scattered distribution of nodal points. Copyright © 2009 John Wiley & Sons, Ltd.

Spurious oscillations occur in the numerical results of convective dominated problems with discontinuities when central interpo-lation schemes are used. Upwind interpolation is necessary to overcome these oscillations. In this work, an upwind scheme is proposed to solve the unsteady convection-diffusion equation using Radial Basis Function (RBF) based Local Hermitian Interpo-lation (LHI) with PDE centres. It is a meshless numerical method based on the interpolation of overlapping RBF systems and also satisfy the governing partial differential equations at certain specified locations. Local hermite interpolation gives symmetric non-singular interpolation matrix which can be inverted easily to solve the system of equations. The scheme is implemented to unsteady benchmark problems and validated against the corresponding analytical solutions. Comparisons with the benchmark solutions show that the proposed upwind scheme is stable and produces significantly accurate results especially for convection dominated problems.

A higher-order compact scheme is combined with an accelerated multigrid method to solve the energy equation in a spherical polar coordinate system. The steady forced convective heat transfer from a sphere which is under the influence of an external magnetic field is simulated. The convection terms in the energy equation are handled in a comprehensive way avoiding complications in the calculations. The angular variation of the Nusselt number and mean Nusselt number are calculated and compared with recent experimental results. Upon applying the magnetic field, a slight degradation of the heat transfer is found for moderate values of the interaction parameter N, and for high values of N an increase in the heat transfer is observed leading to a nonlinear behavior. The speedy convergence of the solution using the multigrid method and accelerated multigrid method is illustrated. Copyright © 2012, Kent State University.

RBF based grid-free scheme with PDE centres is experimented in this work for solving Convection-Diffusion Equations (CDE), a simplified model of the Navier-Stokes equations. For convection dominated problems, very few integration schemes can give converged solutions for the entire range of diffusivity wherein sharp layers are expected in the solutions and accurate computation of these layers is a big challenge for most of the numerical schemes. Radial Basis Function (RBF) based Local Hermitian Interpolation (LHI) with PDE centres is one such integration scheme which has some built in upwind effect and hence may be a good solver for the convection dominated problems. In the present work, to get convergent solutions consistently for small diffusion parameters, an explicit upwinding is also introduced in to the RBF based scheme with PDE centres, which was initially used to solve some time dependent problems in [10]. RBF based numerical schemes are one type of grid free numerical schemes based on the radial distances and hence very easy to use in high dimensional problems. In this work, the RBF scheme, with different upwind biasing, is used to a variety of steady benchmark problems with continuous and discontinuous boundary data and validated against the corresponding exact solutions. Comparisons of the solutions of the convective dominant benchmark problems show that the upwind biasing either in source centres or PDE centres gives convergent solutions consistently and is stable without any oscillations especially for problems with discontinuities in the boundary conditions. It is observed that the accuracy of the solutions is better than the solutions of other standard integration schemes particularly when the computations are carried out with fewer centers.

A numerical study of the natural convection heat transfer of cold water, having the density inversion between two isothermal eccentric horizontal cylinders is studied. A general code is developed for the body fitted coordinate system. This procedure transforms an arbitrarily shaped physical domain into a rectangular (square) domain. The governing equations in this computational domain are solved by the upwind finite difference scheme. The numerical solutions are obtained for a Rayleigh number (Ra) ranging between 103-105, a Prandtl number (Pr) 12.0 and inversion parameter (γ) 0, - 1 and - 2. The affect of the radius ratio (R) on the flow patterns and heat transfer coefficients is studied by taking the Radius ratio as 1.5 and 2. The eccentricity affect is studied by moving the center of the inner cylinder horizontally and vertically (both positive and negative directions) with respect to the center of the outer cylinder. For the cases considered in the present study, it is again for γ = - 1, the minimum heat transfer is observed like in the case of concentric annulus.

A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element. Copyright © 1994 John Wiley & Sons, Ltd

A steady, viscous, incompressible flow past a circular cylinder is studied numerically at moderately high Reynolds numbers. A variable shear flow with velocity curvature factor G is taken as the incident flow. The drag coefficient is calculated at Re = 1000 and 2000 with G = 0, 0.1 and 1.0. The results for G = 0, which correspond to uniform flow, are compared with the existing results for Reynolds numbers upto 500. The non-zero curvature is found to affect the breadth of the wake bubble, the separation angle and the drag coefficient.

An iterative inverse design methodology is used to design gas turbine blades for the prescribed flow conditions. The input flow parameter considered here is the pressure distribution along the suction and pressure surfaces of the blade. The flow is regarded as inviscid. A guess blade is presumed and the flow analysis over the blade is determined using the existing commercial software. In case of mismatch of the flow parameters, the guessed profile surface is considered as a permeable membrane and the normal velocity on the blade surface is computed by conservation of momentum flux approach. The computed normal velocity is used to revise the blade geometry by mass conservation principle till the flow parameters converge. A few geometric constraints are enforced on the model to avoid quixotic blade model. The validation of the above method is being done using NACA profiles. The robustness of the method is verified by using various combinations of NACA blade profiles, where different initial guessed profiles are taken for the same prescribed pressure distribution. This approach can be extended to three dimensional cases.To incorporate the complications attached with the three dimensional flows, three two dimensional sections can be considered on the blade geometry namely at hub, mid span and tip.

In the present investigation, the newly developed Higher Order Semi-Compact (HOSC) finite difference scheme has been tested for its capability in capturing the very complex flow phenomenon of unsteady flow past a rotating and translating circular cylinder. The physical problem has been modeled in stream function and vorticity formulation and the obtained governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle the non-rectangular geometry of the problem. Qualitative and quantitative comparisons have been done at low-rotation parameters and found that the results obtained are in excellent agreement with the existing literature. Then simulations have been carried out at high-rotation parameters and noticed that the HOSC scheme is able to simulate some of the flow features known experimentally but not simulated numerically to the present date. © Springer Science+Business Media, LLC 2007.