Direct and Large Eddy Simulations Using the SIMPLE Algorithm

REFERENCES

• E. Balaras , C. Benocci , and U. Piomelli , Finite-Difference Computations of High Reynolds Number Flows Using the Dynamic Subgrid-Scale Model , Theor. Comp. Fluid Dyn. , vol. 7 , no. 3 , pp. 207 – 216 , 1995 .
   Web of Science ®Google Scholar
• J. Bardina , J. H. Ferziger, and W. C. Reynolds, Improved Turbulence Models Based on LES of Homogeneous Incompressible Turbulent Flows, Department of Mechanical Engineering, Report No. TF-19, Stanford University, Stanford, CA, 1984.
   Google Scholar
• T. Brandt , A Priori Tests on Numerical Errors in Large Eddy Simulation Using Finite Differences and Explicit Filtering , Int. J. Numer. Meth. Fl. , vol. 51 , no. 6 , pp. 635 – 657 , 2006 .
   Web of Science ®Google Scholar
• M. Germano , U. Piomelli , P. Moin , and W. H. Cabot , A Dynamic Subgrid-Scale Eddy Viscosity Model , Phys. Fluids A , vol. 3 , no. 7 , pp. 1760 – 1765 , 1991 .
   Web of Science ®Google Scholar
• O. Desjardina , G. Blanquart , G. Balarac , and H. Pitsch , High Order Conservative Finite Difference Scheme for Variable Density Low Mach Number Turbulent Flows , J. Comput. Phys. , vol. 227 , no. 15 , pp. 7125 – 7159 , 2008 .
   Google Scholar
• B. J. Geurts , Elements of Direct and Large- Eddy Simulation , R. T. Edward, 2004.
   Google Scholar
• P. Moin and J. Kim , Numerical Investigation of Turbulent Channel Flow , J. Fluid Mech. , vol. 118 , pp. 341 – 377 , 1982 .
   Web of Science ®Google Scholar
• B. Song , G. R. Liu , and R. S. Amano , Applications of a Higher-Order Bounded Numerical Scheme to Turbulent Flows , Int. J. Numer. Meth. Fl. , vol. 35 , pp. 371 – 394 , 2001 .
   Web of Science ®Google Scholar
• A. V. Trofimova , A. E. Tejada-Martinez , K. E. Jansen , and R. T. Lahey Jr ., Direct Numerical Simulation of Turbulent Channel Flows Using a Stabilized Finite Element Method , Comput. Fluids , vol. 38 , no. 4 , pp. 924 – 938 , 2009 .
   Web of Science ®Google Scholar
• L. Y. Hu , L. X. Zhou , and Y. H. Luo , Large-Eddy Simulation of the Sydney Swirling NonPremixed Flame and Validation of Several Subgrid-Scale Models , Numer. Heat Transfer, B , vol. 53 , no. 1 , 2008 .
   Google Scholar
• S. L. Rani , C. E. Smith , and A. C. Nix , Boundary-Layer Equation-Based Wall Model for Large-Eddy Simulation of Turbulent Flows with Wall Heat Transfer , Numer. Heat Transfer, B , vol. 55 , no. 2 , 2009 .
   Google Scholar
• G. E. Lau , G. H. Yeoh , V. Timchenko , and J. A. Reizes , Large-Eddy Simulation of Turbulent Natural Convection in Vertical Parallel-Plate Channels , Numer. Heat Transfer, B , vol. 59 , no. 4 , 2011 .
   Google Scholar
• M. M. Rai and P. Moin , Direct Simulations of Turbulent Flow Using Finite-Difference Schemes, J. Comput. Phys. , vol. 96, no. 1, pp. 15–53, 1991.
   Google Scholar
• F. M. Najjar and D. K. Tafti , Evaluation of the Dynamic Subgrid-Scale Stress Model in Finite Differenced LES: Effects of Grid Resolution and Inhomogeneous Test Filtering, Symposium on LES and DNS of Turbulent Flow, 242 FED, pp. 229–236, 1996.
   Google Scholar
• F. M. Najjar and D. K. Tafti , Study of Discrete Test Filters and Finite Difference Approximations for the Dynamic Subgrid-Scale Stress Model , Phys. Fluids , vol. 8 , no. 4 , pp. 1076 – 1088 , 1996 .
   Web of Science ®Google Scholar
• D. Tafti , Comparison of Some Upwind-Biased High-Order Formulations with a Second-Order Central-Difference Scheme for Time Integration of the Incompressible Navier-Stokes Equations , Comput. Fluids , vol. 25 , no. 7 , pp. 647 – 665 , 1996 .
   Web of Science ®Google Scholar
• J. G. M. Eggels , F. Unger , M. H. Weiss , J. Westerweel , R. J. Adrian , R. Friedrich , and F. T. M. Nieuwstadt , Fully Developed Turbulent Pipe Flow: A Comparison Between Direct Numerical Simulation and Experiment , J. Fluid Mech. , vol. 268 , pp. 175 – 209 , 1994 .
   Web of Science ®Google Scholar
• P. Majander and T. Siikonen , Evaluation of Smagorinsky-Based Subgrid-Scale Models in a Finite- Volume Computation , Int. J. Numer. Meth. Fl. , vol. 40 , pp. 735 – 774 , 2002 .
   Google Scholar
• J. Meyers , B. J. Geurts , and P. Sagaut , A Computational Error-Assessment of Central Finite-Volume Discretizations in Large-Eddy Simulation Using a Smagorinsky Model , J. Comput. Phys. , vol. 227 , pp. 156 – 173 , 2007 .
   Web of Science ®Google Scholar
• P. Sagaut , and M. Ciardi , A Finite-Volume Variational Multiscale Method Coupled with a Discrete Interpolation Filter for Large-Eddy Simulation of Isotropic Turbulence and Fully Developed Channel Flow , Phys. Fluids , vol. 18 , 115101 , 2006 .
   Google Scholar
• P. K. Subbareddy , and G. V. Candler , A Fully Discrete , Kinetic Energy Consistent Finite-Volume Scheme for Compressible Flows , J. Comput. Phys. , vol. 228 , no. 5 , pp. 1347 – 1364 , 2009 .
   Web of Science ®Google Scholar
• X. Xu , J. S. Lee , and R. H. Pletcher , A Compressible Finite Volume Formulation for Large Eddy Simulation of Turbulent Pipe Flows at Low Mach Number in Cartesian Coordinates , J. Comput. Phys. , vol. 203 , no. 1 , pp. 22 – 48 , 2005 .
   Google Scholar
• P. S. Zandonade , J. A. Langford , and R. D. Moser , Finite-Volume Optimal Large-Eddy Simulation of Isotropic Turbulence , Phys. Fluids , vol. 16 , no. 7 , pp. 2255 – 2271 , 2004 .
   Google Scholar
• L. Xu , G. Cui , C. Xu , Z. Wang , Z. Zhang , and N. Chen , High Accurate Finite Volume Method for Large Eddy Simulation of Complex Turbulent Flows , Int. J. Turbo. Jet Eng. , vol. 23 , no. 3 , pp. 191 – 210 , 2006 .
   Google Scholar
• J. Kim and P. Moin , Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 59 , no. 2 , pp. 308 – 323 , 1985 .
   Web of Science ®Google Scholar
• H. Choi and P. Moin , Effects of Computational Time Step on Numerical Solutions of Turbulent Flow , J. Comput. Phys. , vol. 113 , pp. 1 – 4 , 1994 .
   Web of Science ®Google Scholar
• J. Kim , P. Moin , and R. Moser , Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number , J. Fluid Mech. , vol. 177 , pp. 133 – 166 , 1987 .
   Web of Science ®Google Scholar
• Y. Hou and K. Mahesh , A Robust Colocated Implicit Algorithm for Direct Numerical Simulation of Compressible Turbulent Flows , J. Comput. Phys. , vol. 205 , pp. 205 – 221 , 2005 .
   Web of Science ®Google Scholar
• T. Park , Effects of Time-Integration Method in a Large-Eddy Simulation Using the PISO Algorithm: Part I- Flow Field , Numer. Heat Transfer A. , vol. 50 , no. 3 , pp. 229 – 245 , 2006 .
   Web of Science ®Google Scholar
• J. H. Ferziger and M. Peric , Computational Methods for Fluid Dynamics , Springer-Verlag , New York , 1999 .
   Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp., New York, 1980.
   Google Scholar
• J. B. Perot , Comments on the Fractional Step Method , J. Comput. Phys. , vol. 121 , no. 1 , pp. 190 – 191 , 1995 .
   Google Scholar
• J. B. Perot , An Analysis of the Fractional Step Method, J. Comput. Phys. , vol. 108, no. 1, pp. 51–58, 1993.
   Web of Science ®Google Scholar
• C. Pozrikidis , On the Relationship Between the Pressure and the Projection Function in the Numerical Computation of Viscous Incompressible Flow , Eur. J. Mech. B-Fluid. , vol. 22 , no. 2 , pp. 105 – 121 , 2003 .
   Google Scholar
• Y. Wang and Y. Ren , Accuracy Analysis of Approximate Projection Methods for Solving Incompressible Flows , Qinghua Daxue Xuebao/J. of Tsinghua U. , vol. 48 , no. 2 , pp. 280 – 284 , 2008 .
   Google Scholar
• S. V. Patankar , and D. B. Spalding , A Calculation Procedure for Heat , Mass and Momentum Transfer in Three-Dimensional Parabolic Flows , Int. J. Heat Mass Transfer , vol. 15 , pp. 1767 – 1806 , 1972 .
   Web of Science ®Google Scholar
• B. R. Baliga and S. V. Patankar , A Control-Volume Finite Element Method for Two- Dimensional Incompressible Fluid Flow and Heat Transfer , Numer. Heat Transfer, Part B , vol. 6 , pp. 245 – 261 , 1983 .
   Google Scholar
• I. Demirdzic , and S. Muzaferija , Numerical Method for Coupled Fluid Flow , Heat Transfer and Stress Analysis Using Unstructured Moving Meshes with Cells of Arbitrary Topology , Comput. Methods Appl. Mech. Eng. , vol. 125 , pp. 235 – 255 , 1995 .
   Web of Science ®Google Scholar
• C. F. Hsu , A Curvilinear-Coordinate Method for Momentum, Heat and Mass Transfer in Domains of Irregular Geometry, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 1981.
   Google Scholar
• K. C. Karki and S. V. Patankar , Calculation Procedure for Viscous Incompressible Flows in Complex Geometries , Numer. Heat Transfer, Part B , vol. 14 , pp. 295 – 307 , 1986 .
   Google Scholar
• F. S. Lien , A Pressure-Based Unstructured Grid Method for All-Speed Flows , Int. J. Numer. Methods Fluids , vol. 33 , pp. 355 – 374 , 2000 .
   Web of Science ®Google Scholar
• C. R. Maliska and G. D. Raithby , A Method for Computing Three-Dimensional Flows Using Non-Orthogonal Boundary-Fitted Coordinates , Int. J. Numer. Methods Fluids , vol. 4 , pp. 519 – 537 , 1984 .
   Web of Science ®Google Scholar
• S. R. Mathur and J. Y. Murthy , A Pressure-Based Method for Unstructured Meshes , Numer. Heat Transfer A , vol. 31 , pp. 195 – 216 , 1997 .
   Google Scholar
• S. V. Patankar , Calculation Procedure for Two-Dimensional Elliptic Situations , Numer. Heat Transfer, Part B , vol. 4 , no. 4 , pp. 409 – 425 , 1981 .
   Google Scholar
• C. Prakash and S. V. Patankar , A Control-Volume-Based Finite-Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer, Part A , vol. 8 , pp. 259 – 280 , 1985 .
   Google Scholar
• W. Shyy , S. S. Tong , and S. M. Correa , Numerical Recirculating Flow Calculation Using a Body-Fitted Coordinate System , Numer. Heat Transfer, Part B , vol. 8 , pp. 99 – 113 , 1985 .
   Web of Science ®Google Scholar
• M.-J. Ni and M. A. Abdou , A Bridge Between Projection Methods and SIMPLE Type Methods for Incompressible Navier–Stokes Equations , Int. J. Numer. Meth. Eng. , vol. 72 , pp. 1490 – 1512 , 2007 .
   Web of Science ®Google Scholar
• H. Suzuki and H. Usui , Direct Numerical Simulation of a Turbulent Duct Flow by High-Ordered Scheme for SIMPLE, The 13th Japanese Symposium of Computational Fluid Dynamics (JSCFD), pp. B04–B03. Tokyo, Japan, 1999.
   Google Scholar
• C. F. Lange , M. Schafer , and F. Durst , Local Block Refinement with a Multigrid Flow Solver , Int. J. Numer. Methods Fluids , vol. 38 , pp. 21 – 41 , 2002 .
   Google Scholar
• F. Moukalled and M. Darwish , A High-Resolution Pressure Based Algorithm for Fluid Flow at All Speeds , J. Comput. Phys. , vol. 168 , pp. 101 – 133 , 2001 .
   Web of Science ®Google Scholar
• M. Ijaz and N. K. Anand , Simulation of Unsteady Incompressible Viscous Flow Using Higher-Order Implicit Runge-Kutta Methods-Staggered Grid , Numer. Heat Transfer B , vol. 52 , pp. 471 – 488 , 2007 .
   Web of Science ®Google Scholar
• S. Acharya , B. R. Baliga , K. Karki , J. Y. Murthy , C. Prakash , and S. P. Vanka , Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics, J. Heat Transfer , vol. 129, pp. 407–424, 2007.
   Web of Science ®Google Scholar
• B. P. Leonard , A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation , Comput. Method. Appl. M. , vol. 19 , pp. 59 – 98 , 1979 .
   Web of Science ®Google Scholar
• M. Lesieur , Turbulence in Fluids, , 4th ed. , Springer , London , 2008 .
   Google Scholar
• P. Sagaut , Large Eddy Simulation for Incompressible Flows, , 3rd ed. , Springer-Verlag , Berlin , 2006 .
   Google Scholar
• U. Piomelli , High Reynolds Number Calculations Using the Dynamic Subgrid-Scale Stress Model , Phys. Fluids A , vol. 5 , no. 6 , 1993 .
   Google Scholar
• Y. Zang , R. L. Street , and J. R. Koseff , A Dynamic Mixed Subgrid Model and Its Application to Turbulent Recirculation Flows , Physics Fluids A , vol. 5 , no. 12 , 1993 .
   Google Scholar
• S. V. Patankar , C. Liu , and E. Sparrow , Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area , ASME J. Heat Transfer , vol. 99 , pp. 180 – 186 , 1977 .
   Web of Science ®Google Scholar
• H. Montazeri , A Consistent Numerical Method for Simulating Interfacial Turbulent Flows, Ph.D. thesis, the University of Toronto, Toronto, Canada, 2010.
   Google Scholar
• S. C. Chapra and R. P. Canale , Numerical Methods for Engineering , 6th ed. , McGrawHill , New York , 2010 .
   Google Scholar
• J. M. C. Pereira and J. C. F. Pereira , Fourier Analysis of Several Finite Difference Schemes for the One-Dimensional Unsteady Convection–Diffusion Equation , Int. J. Numer. Meth. Fluids , vol. 36 , pp. 417 – 439 , 2001 .
   Web of Science ®Google Scholar
• Compaq Extended Math Library Reference Guide , Compaq Computer Corporation Houston, Texas, Jan. 2001.
   Google Scholar
• H. Abe , H. Kawamura , and Y. Matsuo , Direct Numerical Simulation of a Fully Developed Turbulent Channel Flow with Respect to Reynolds Number Dependence , ASME J. Fluids Eng. , vol. 123 , pp. 382 – 393 , 2001 .
   Web of Science ®Google Scholar