Literature review on pressure–velocity decoupling algorithms applied to built-environment CFD simulation

Abstract For decades, computational fluid dynamics (CFD) has been applied to built-environment related simulations such as those of building ventilation, indoor airflow, and contaminant transportation. The pressure–velocity decoupling algorithm employed in CFD to solve momentum equation(s) exerts significant influence on the convergence speed and computational resource requirement. In order to identify the opportunities to improve CFD performance for built-environment simulation, a review is conducted on the commonly used pressure–velocity decoupling algorithms in indoor environment CFD modeling, with the aim of summarizing the general status and trends of the application and development of the decoupling algorithms. The study categorizes the primary algorithms based on the advantages and disadvantages of each reviewed algorithm and the applications of each analyzed algorithm. The review indicates an explicit prevalence of the usage of the SIMPLE algorithm and its variants in indoor-environment CFD simulation, which is a combined outcome of the superiority of such algorithms and their wide availability in commonly used CFD software. However, each algorithm variant has applicable engineering fields unique to it. The study also identifies that a few less-commonly used algorithms in both research and commercial CFD software, such as the projection algorithm, reveal certain advantages in terms of convergence and accuracy performance. These algorithms exhibit significant potential for transforming the conventional pressure–velocity decoupling algorithm into approaches that can more efficiently solve flow-governing momentum equation(s), specifically for built-environment CFD simulation.

[1]  R. Yin,et al.  COMPARISON OF FOUR ALGORITHMS FOR SOLVING PRESSURE- VELOCITY LINKED EQUATIONS IN SIMULATING ATRIUM FIRE , 2003 .

[2]  Stephen R. Turnock,et al.  Grid resolution for the simulation of sloshing using CFD , 2007 .

[3]  Jie Shen,et al.  On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes , 1996, Math. Comput..

[4]  William E. Pracht,et al.  A numerical method for calculating transient creep flows , 1971 .

[5]  Robert L. Street,et al.  SUMMAC - A NUMERICAL MODEL FOR WATER WAVES. , 1970 .

[6]  Jian‐Guo Liu,et al.  Projection method I: convergence and numerical boundary layers , 1995 .

[7]  Edouard Audi Comparison of pressure-velocity coupling schemes for 2D flow problems , 2009, 2009 International Conference on Advances in Computational Tools for Engineering Applications.

[8]  R. Courant,et al.  On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .

[9]  F. Durst,et al.  Study of Laminar, Unsteady Piston-Cylinder Flows , 1993 .

[10]  F. Moukalled,et al.  A coupled finite volume solver for the solution of incompressible flows on unstructured grids , 2009, J. Comput. Phys..

[11]  John Bussoletti CFD calibration and validation - The challenges of correlating computational model results with test data , 1994 .

[12]  J. A. Viecelli,et al.  A computing method for incompressible flows bounded by moving walls , 1971 .

[13]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[14]  A. D. Gosman,et al.  Numerical Prediction of Turbulent Flow over Surface-Mounted Ribs , 1985 .

[15]  Michael S. Engelman,et al.  Segregated finite element algorithms for the numerical solution of large‐scale incompressible flow problems , 1993 .

[16]  Huankun Fu High Order Numerical Schemes For PDEs And Applications To CFD , 2014 .

[17]  Jie Shen,et al.  A new class of truly consistent splitting schemes for incompressible flows , 2003 .

[18]  S. Orszag,et al.  Boundary conditions for incompressible flows , 1986 .

[19]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[20]  Asif Usmani,et al.  Finite Element Analysis for Transient Non-Newtonian Flow , 1999 .

[21]  Jos Stam,et al.  Diffraction shaders , 1999, SIGGRAPH.

[22]  S. Vanka Block-implicit multigrid solution of Navier-Stokes equations in primitive variables , 1986 .

[23]  Tienfuan Kerh,et al.  Finite element analysis of fluid motion with an oscillating structural system , 1998 .

[24]  Wei Liu,et al.  Development of a fast fluid dynamics-based adjoint method for the inverse design of indoor environments , 2017 .

[25]  Qingyan Chen,et al.  A Procedure for Verification, Validation, and Reporting of Indoor Environment CFD Analyses , 2002 .

[26]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[27]  Jie Shen,et al.  An overview of projection methods for incompressible flows , 2006 .

[28]  S. Orszag,et al.  High-order splitting methods for the incompressible Navier-Stokes equations , 1991 .

[29]  Wan Ki Chow,et al.  Comparison of the algorithms PISO and simpler for solving pressure-velocity linked equations in simulating compartmental fire , 1997 .

[30]  George D. Raithby,et al.  Solution of the incompressible mass and momentum equations by application of a coupled equation line solver , 1985 .

[31]  John C. Strikwerda,et al.  The Accuracy of the Fractional Step Method , 1999, SIAM J. Numer. Anal..

[32]  C. W. Hirt,et al.  SOLA: a numerical solution algorithm for transient fluid flows , 1975 .

[33]  K. Goda,et al.  A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows , 1979 .

[34]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[35]  S. Acharya,et al.  Comparison of the Piso, Simpler, and Simplec Algorithms for the Treatment of the Pressure-Velocity Coupling in Steady Flow Problems , 1986 .

[36]  Frans N. van de Vosse,et al.  An approximate projec-tion scheme for incompressible ow using spectral elements , 1996 .

[37]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[38]  Ali Cemal Benim,et al.  A segregated formulation of Navier-Stokes equations with finite elements , 1986 .

[39]  R. Temam Une méthode d'approximation de la solution des équations de Navier-Stokes , 1968 .

[40]  Yu Xue,et al.  New semi-Lagrangian-based PISO method for fast and accurate indoor environment modeling , 2016 .

[41]  Andrew Pollard,et al.  COMPARISON OF PRESSURE-VELOCITY COUPLING SOLUTION ALGORITHMS , 1985 .

[42]  Zhiqiang Zhai,et al.  Advances in building simulation and computational techniques: A review between 1987 and 2014 , 2016 .

[43]  Haidong Wang,et al.  Fast CFD simulation method for indoor environment modeling , 2013 .

[44]  Young‐Il Lim,et al.  Distributed Dynamic Models and Computational Fluid Dynamics , 2008 .

[45]  Peter V. Nielsen,et al.  Fifty years of CFD for room air distribution , 2015 .

[46]  Q Chen,et al.  Real-time or faster-than-real-time simulation of airflow in buildings. , 2009, Indoor air.

[47]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[48]  D. Spalding,et al.  Two numerical methods for three-dimensional boundary layers , 1972 .

[49]  G. D. Raithby,et al.  The segregated approach to predicting viscous compressible fluid flows , 1986 .

[50]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[51]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[52]  A. D. Gosman,et al.  The computation of flow in a spirally fluted tube , 1984 .

[53]  J. Kan A second-order accurate pressure correction scheme for viscous incompressible flow , 1986 .

[54]  Zhiping Wang Phase-field Simulation of Pure Material Dendritic Growth Based on Sola Algorithm in Force Laminar Flow , 2010 .

[55]  J. B. Perot,et al.  An analysis of the fractional step method , 1993 .

[56]  A. Pollard,et al.  Finite volume methods for laminar and turbulent flows using a penalty function approach , 1994 .

[57]  Parviz Moin,et al.  On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries , 1980 .

[58]  Dominique Pelletier,et al.  FINITE ELEMENT METHOD FOR COMPUTING TURBULENT PROPELLER FLOW , 1991 .

[59]  I. E. Barton,et al.  Comparison of SIMPLE‐ and PISO‐type algorithms for transient flows , 1998 .

[60]  Akshai K. Runchal,et al.  Brian Spalding: CFD and reality – A personal recollection , 2009 .

[61]  宮田 秀明,et al.  Numerical Analysis of Free Surface Shock Waves around Bow by Modified MAC-Method : First Report , 1983 .

[62]  G. Hauke,et al.  A segregated method for compressible flow computation. Part II: general divariant compressible flows , 2005 .

[63]  D. Wilcox Turbulence modeling for CFD , 1993 .

[64]  M. Minion,et al.  Accurate projection methods for the incompressible Navier—Stokes equations , 2001 .

[65]  Jean-Luc Guermond,et al.  Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale , 1999 .

[66]  A. Chorin A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[67]  Grégoire Pianet,et al.  Local penalty methods for flows interacting with moving solids at high Reynolds numbers , 2007 .

[68]  Shuzo Murakami,et al.  Environmental design of outdoor climate based on CFD , 2006 .

[69]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .