IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

In this paper the interaction of a two-dimensional progressive wave train over a submerged rectangular porous breakwater is studied theoretically. For this purpose, the time dependent incompressible Navier-Stokes-Brinkman system is newly derived for wave propagating over submerged breakwater. A staggered grid Finite Volume Method (FVM) is used to solve the Navier-Stokes-Brinkman system. The free surface boundary condition and the interfacial boundary conditions between the water and porous media are in complete form. A Volume-of-Fluid (VOF) methodology is employed to track the free surface. The validity of present model is verified based on the compressions with the existing experimental results. Having verified the accuracy of the numerical model, the effects of several parameters of a wave and a submerged breakwater were systematically investigated. The results indicate that the wave transformations are affected primarily by the breakwater width and the structure permeability. The numerical results also illustrate that for the porous breakwater, an optimum porosity value seems to exist at which the transmitted wave height is minimized. It has been observed that the transmission coefficient decreases as the permeability increases. However, the results indicate that further increase of the structure permeability beyond the optimal value increase the transmission coefficient.

Department of Mathematics

Tamkang Journal of Mathematics

Navier-stokes-brinkman system for interaction of viscous waves with a submerged porous structure

We present an investigation of extrapolation boundary conditions for lattice Boltzmann method (LBM) using asymptotic analysis. Equilibrium and non-equilibrium extrapolation methods for velocity and pressure boundary conditions proposed in the literature were tested numerically in specific cases. We analyse these boundary conditions using asymptotic expansion techniques and show an improvement in the accuracy of the lattice Boltzmann solution. We also present few numerical examples and simulate fluid flow across an unsymmetrically placed stationary cylinder in a channel with steady and unsteady flow conditions. Thus the article demonstrates application of asymptotic analysis to understand properties of extrapolation boundary conditions for LBM and show the flexibility of these boundary conditions for complex fluid flow applications. © 2009 Elsevier Ltd. All rights reserved.

Fulltext

Computers and Mathematics with Applications

Asymptotic analysis of extrapolation boundary conditions for LBM

We consider an isothermal model for the film casting process. The aim of this study is to determine a shape of the die that leads to a uniform thickness of the film. Thanks to a decoupling of the equations for the thickness and the velocities of the film, we are able to solve the reverse thickness equation. This reverse equation describes the dependence of the shape of the die on the desired final thickness. © 2009 Elsevier Ltd. All rights reserved.

GENERAL

Applied Mathematics Letters

Optimal die shape for film casting

We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier-Stokes equations. We control the thickness of the film at the take-up point using the shape of the nozzle and the initial thickness. The control goal consists in finding an even thickness profile. To achieve this goal, we minimize an appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method. The gradient of the cost functional is approximated using the adjoint variables of the problem with fixed film width. Numerical simulations show the applicability of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

International Journal for Numerical Methods in Fluids

Optimal control of film casting processes

A comprehensive study is done to model flow of heat through heat insulators based on materials with high gas content such as solidified foams (e.g., eXtruded PolyStyrene foams, Expanded PolyStyrene foam), cellular glass, etc. The actual internal cell-like structure of such an insulator is replicated by regularly shaped gas pockets, which are separated from each other by thin rims of solid materials. The first model focuses on heat flow across the insulator caused by conduction and convection. Subsequently, the effect of radiation is also studied. Several numerical results are presented and computational results are compared with experimentally measured data. © 2007 by the Massachusetts Institute of Technology.

Studies in Applied Mathematics

Study of heat flow through highly porous heat insulators

In this paper, we describe the mathematical modeling of heat flow across a glass fiber medium. Using different mathematical models we try to explain the porosity dependence of the heat flow which is observed in experiments. © 2005 Elsevier Ltd. All rights reserved.

Mathematical and Computer Modelling

Understanding the porosity dependence of heat flux through glass fiber insulation

This paper suggests a method for automating the process of checking for a sufficiently matching sole pattern in a given collection of sole patterns. It may take up to weeks to manually do the same, in the industry. We describe the method of finding the best match from a given set using a procedure, the basis of which is the Karhunen-Loueve transform (KLT), involving a projection onto a subspace spanned by the eigenpatterns corresponding to the largest few eigenvalues. The patterns are first scanned, stored in picture file format, and cleaned up so that they consist of a black sole and a white background, to minimize unnecessary information content. Their centers of masses are aligned and principal moment of inertia axes are arranged vertically to maximize correlation between these pictures. The eigenpatterns are found for this collection of pictures. To find the best match for the new sole pattern, its projection onto the lesser-dimensional subspace spanned by the eigenpatterns is found. The projected pattern can be decomposed into a weighted sum of the eigenpatterns. The best match is found using a minimum distance criterion in this space. This method is suitable for any highly correlated image database. © 2003 Elsevier Science Ltd. All rights reserved.

Pattern search in a shoe sole image database using eigenpatterns

In this paper, we present a recursive algorithm for the construction of general matrix Padé approximants. The two main algorithms involved here are MAPORES (MAtrix POlynomial REmainder Sequence), which is a recursive one, and MAPADAC (MAtrix Padé Approximants by Divide-And-Conquer). MAPADAC is based on the divide-and-conquer version of an earlier work on matrix Padé extended Euclidean algorithm (MAPEA). The algorithm is also capable of computing the Padé approximants for the abnormal power series possessing matrix coefficients. An efficient Pascal procedure for implementation of the same is provided here. The different steps involved in the entire approach are explained in detail and illustrated by a few explicit examples. © 1989.

A recursive algorithm for matrix Padé approximants-the divide-and-conquer approach

Work on Padé or Padé-type approximants ultimately involves the explicitdetermination of the polynomials forming the numerator and denominator of rational functions. These exist in the literature useful algorithms for constructing the polynomials when the starting coefficients of the given power series are of the ordinary kind. However, when one has the matrix coefficients forthe series, it becomes necessary to extend the procedure taking into account the special nature of the various operations. In this paper we present a new application of the extended Euclidean algorithm in order to obtain the sets of complete matrix Padé approximants. Also, an efficient Pascal procedure for implementation of the algorithm is given. In fact, the resulting algorithm generates the elements in the anti-diagonal of the Padé table. The concepts and constructive steps involved in the procedure are explained in detail and illustrated by a few suitable examples to show (i) how the algorithm works in general and (ii) the usefulness of the entire approach. © 1988.