Review on thermal energy storage with phase change: materials, heat transfer analysis and applications

Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems. The paper is addressed to readers who already have experience with SIMPLE or its variants.

Enhancements of the simple method for predicting incompressible fluid flows

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

http://www.inf.ufes.br/~luciac/comcie/JFNK-Knoll.pdf

Jacobian-free Newton-Krylov methods: a survey of approaches and applications

The accuracy of numerical simulation algorithms is one of main concerns in modern Computational Fluid Dynamics. Development of new and more accurate mathematical models requires an insight into the problem of numerical errors. In order to construct an estimate of the solution error in Finite Volume calculations, it is first necessary to examine its sources. Discretisation errors can be divided into two groups: errors caused by the discretisation of the solution domain and equation discretisation errors. The first group includes insufficient mesh resolution, mesh skewness and non-orthogonality. In the case of the second order Finite Volume method, equation discretisation errors are represented through numerical diffusion. Numerical diffusion coefficients from the discretisation of the convection term and the temporal derivative are derived. In an attempt to reduce numerical diffusion from the convection term, a new stabilised and bounded second-order differencing scheme is proposed. Three new methods of error estimation are presented. The Direct Taylor Series Error estimate is based on the Taylor series truncation error analysis. It is set up to enable single-mesh single-run error estimation. The Moment Error estimate derives the solution error from the cell imbalance in higher moments of the solution. A suitable normalisation is used to estimate the error magnitude. The Residual Error estimate is based on the local inconsistency between face interpolation and volume integration. Extensions of the method to transient flows and the Local Residual Problem error estimate are also given. Finally, an automatic error-controlled adaptive mesh refinement algorithm is set up in order to automatically produce a solution of pre-determined accuracy. It uses mesh refinement and unrefinement to control the local error magnitude. The method is tested on several characteristic flow situations, ranging from incompressible to supersonic flows, for both steady-state and transient problems.

Error analysis and estimation for the finite volume method with applications to fluid flows

Semidirect solution techniques can be an effective alternative to the more conventional iterative approaches used in many finite difference methods. This paper summarises several semidirect techniques which generally have not been applied to the Navier-Stokes and energy equations in finite difference form. The methods presented use both successive substitution and Jacobian-based updates as well as two variations of Broyden's full matrix update. A hybrid method is also presented, as is a norm-reducing search technique that can be used to enhance the convergence characteristic of any semidirect approach. See also the following Abstract.

Robust semidirect finite difference methods for solving the Navier–Stokes and energy equations

Thermal interactions among the confining walls of a turbulent recirculating flow

The capabilities of a new curvilinear coordinate-based calculation procedure for incompressible flows are demonstrated by its application to a variety of test problems. The results are compared with the results of independent numerical and experimental studies available in the literature. These comparisons indicate that the proposed scheme can be successfully used to predict fluid flow and heat transfer phenomena in complex configurations.

Solution of some two-dimensional incompressible flow problems using a curvilinear coordinate system based calculation procedure

A simple non-gray gas model for use in radiation computations is proposed. This is based on the idea of k distribution, or reordering the highly irregular variation of absorption coefficient to obtain a smooth function. In the present approach, a methodology to obtain the reordered distribution from a wide-band model is presented, which is simpler than previous methods. Several test problems, including nonisothermal and inhomogeneous media, are solved using the model. The validity of the approach is tested by comparing solutions to radiation problems with previously published results.

A simple approach to non-gray gas modeling

/pdf/cfd-model-for-jet-fan-ventilation-systems-1zwls8nvdc.pdf

Suhas V. Patankar

Papers

Robust semidirect finite difference methods for solving the Navier–Stokes and energy equations

Thermal interactions among the confining walls of a turbulent recirculating flow

Solution of some two-dimensional incompressible flow problems using a curvilinear coordinate system based calculation procedure

A simple approach to non-gray gas modeling

Cfd model for jet fan ventilation systems