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

Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area

A calculation method based on the control-volume approach has been developed for solving two-dimensional elliptic problems involving fluid flow and heat and mass transfer. The main features of the method include a power-law formulation for the combined convection-diffusion Influence, an equation-solving scheme that consists of a block-correction method coupled with a line-by-line procedure, and a new algorithm for handling the interlinkage between the momentum and continuity equations. Although the method is described for steady two-dimensional situations, its extension to unsteady flows and three-dimensional problems is very straightforward.

a Calculation Procedure for Two-Dimensional Elliptic Situations

This chapter presents a finite-volume (FV) method for computing radiation heat transfer processes The main ingredients of the calculation procedure were presented by Chai et al [1] The resulting method has been tested, refined and extended to account for various geometrical and physical complexities

Finite volume method for radiation heat transfer

A general numerical method for convection-diffusion problems is presented The method is formulated for two-dimensional problems, but its key Ideas can be extended to three-dimensional problems The calculation domain is first divided into three-node triangular elements, and then polygonal control volumes are constructed by joining the centroids of the elements to the midpoints of the corresponding sides In each element, the dependent variable is interpolated exponentially in the direction of the element-average velocity vector and linearly in the direction normal to it These interpolation functions respond to an element Peclet number and become linear when it approaches zero The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes The proposed method has the conservative property, can handle problems in the whole range of Peclet numbers, and avoids the false-diffusion difficulties that commonly afflict o

A new finite-element formulation for convection-diffusion problems

The formulation of a general numerical method for two-dimensional incompressible flow and heat transfer in irregular-shaped domains is presented. The calculation domain is first divided into six-node macroelements. Then each macroelement is divided into four three-node triangular subelements. Polygonal control volumes are associated with the nodes of these elements. All dependent variables other than pressure are stored at the nodes of the subelements, and they are interpolated by functions that respond appropriately to an element Peclet number and the direction of an element-averaged velocity vector. The pressure is stored only at the vertices of the macroelements and is interpolated linearly in these elements. The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes. An iterative procedure akin to SIMPLER is used to solve the discretization equations.

Suhas V. Patankar

Papers

Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area

a Calculation Procedure for Two-Dimensional Elliptic Situations

Finite volume method for radiation heat transfer

A new finite-element formulation for convection-diffusion problems

A control volume finite-element method for two-dimensional fluid flow and heat transfer