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

Recent Developments in the Solution of Radiation Heat Transfer Using the Discrete Ordinates Method

Laminar Heat Transfer of a Radiating Fluid in a Backward Facing Step Flow

A control volume-based finite-element method for solving the Navier-Stokes equations using equal-order velocity-pressure interpolation is presented. Unlike the unequal-order-type methods that compute pressure at much fewer grid points than velocity, the proposed equal-order method calculates velocity and pressure at all the grid points in the domain. The validity of the method is established by applying it to solve some test problems

A control volume based finite element method for solving the Navier-Stokes equations using equal order velocity-pressure interpolation

Computational Analysis of the Vacuum Arc Remelting (VAR) and Electroslag Remelting (ESR) Processes

Three popular spatial differencing schemes for the discrete ordinates method are examined for two-dimensional Cartesian coordinates system. These are a positive, the step, and the diamond schemes. Contrary to the common belief that negative intensities will not occur when fine spatial discretization is used with the diamond scheme, under certain conditions, the diamond scheme will produce negative intensities irrespective of the number of control volums employed. The positive scheme can produce physically unrealistic trends. The diamond and positive schemes are also capable of producing physically unrealistic overshoots. In absorbing-emitting or absorbing-emitting-scattering media, grid refinement can result in negative intensities when the diamond or positive scheme is used.

Suhas V. Patankar

Papers

Recent Developments in the Solution of Radiation Heat Transfer Using the Discrete Ordinates Method

Laminar Heat Transfer of a Radiating Fluid in a Backward Facing Step Flow

A control volume based finite element method for solving the Navier-Stokes equations using equal order velocity-pressure interpolation

Computational Analysis of the Vacuum Arc Remelting (VAR) and Electroslag Remelting (ESR) Processes

An evaluation of three spatial differencing schemes for the discrete ordinates method in participating media