S. Sundar

Understanding the porosity dependence of heat flux through glass fiber insulation

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.

Comparison of Krylov subspace methods with preconditioning techniques for solving boundary value problems

Abstract In this paper, we made an attempt to establish the usefulness of Lanczos solver with preconditioning technique over the preconditioned Conjugate Gradient (CG) solvers. We have presented here a detail comparative study with respect to convergence, speed as well as CPU-time, by considering appropriate boundary value problems.

Newton-preconditioned Krylov subspace solvers for system of nonlinear equations: A numerical experiment

In this paper, we present a numerical comparative study of the Newton-preconditioned Lanczos algorithms and Newton-preconditioned CG-like methods, with respect to convergence speed and CPU-time, by considering appropriate test problems.

Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method

Abstract In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using Lanczos algorithm with a recursive partitioning method as well as the Sturm sequence-bisection method have been discussed. We have also presented the comparison of the numerical results and the CPU-time between the above two methodologies. Our comparative study indicates that the Lanczos with a recursive partitioning method takes relatively less computing time than that of the Sturm sequence-bisection method.

Comparison of Lanczos and CGS solvers for solving numerical heat transfer problems

Abstract In this paper, we have presented a comparative study of the Lanczos solver with out preconditioning and Conjugate Gradient Squared (CGS) solver with preconditioning for solving numerical heat transfer problem. Our comparison is mainly focussed on the convergence and the CPU-time.

Long time behaviour of the solution of a system of equations from new theory of shock dynamics

The new theory of shock dynamics gives a system of n + 2 equations, the solution of which determines the propagation of a discontinuity in the initial condition. For the model equation ut + u ux = 0, the long time behaviour of the solution is investigated for various confined initial data. The suitability of using Pade approximants for the solution is examined. Special exact solutions are obtained.

Asymptotic analysis of extrapolation boundary conditions for LBM

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.

A CASE STUDY WITH THE NEW THEORY OF SHOCK DYNAMICS

Abstract A new theory of shock dynamics (NTSD) with analytic considerations and a numerical solution has already been discussed in Part I and Part II. This paper deals with the numerical simulation of the system of ordinary differential equations of the new theory of shock dynamics for the equation u t + ( u 2 2 ) x = 0 when ux(x, 0) = φ′(x)

A new application of the extended euclidean algorithm for matrix Padé approximants

Abstract Work on Pade or Pade-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 Pade 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 Pade 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.

Study of Heat Flow through Highly Porous Heat Insulators

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.