Hybrid finite element/volume method for 3D incompressible flows with heat transfer

References

• Aliabadi , S. 1994 . Parallel finite element computations in aerospace applications , Thesis (PhD). University of Minnesota .
   Google Scholar
• Aliabadi , S. and Tezduyar , T. E. 1993 . Space-time finite element computation of compressible flows involving moving boundaries and interfaces . Computer Methods in Applied Mechanics and Engineering , 107 : 209 – 223 .
   Web of Science ®Google Scholar
• Aliabadi , S. and Tezduyar , T. E. 2000 . Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces . Computer Methods in Applied Mechanics and Engineering , 190 : 243 – 261 .
   Web of Science ®Google Scholar
• Aliabadi , S. , Abedi , J. and Zellars , B. 2003 . Parallel finite element simulation of mooring forces on floating objects . International Journal for Numerical Methods in Fluids , 41 : 809 – 822 .
   Web of Science ®Google Scholar
• Aliabadi , S. , Akbar , M. and Patel , R. 2010 . Hybrid finite element/volume method for shallow water equations . International Journal of Numerical Methods in Engineering , 83 ( 13 ) : 1719 – 1738 .
   Web of Science ®Google Scholar
• Aliabadi , S. 2002 . Stabilized finite element formulation of buoyancy driven incompressible flows . Journal of Communications in Numerical Methods in Engineering , 18 ( 5 ) : 315 – 324 .
   Web of Science ®Google Scholar
• Aliabadi , S. 2006 . Integrated high performance computational tools for simulations of transport and diffusion of contaminants in urban areas . International Journal of Computational Fluid Dynamics , 20 : 253 – 267 .
   Web of Science ®Google Scholar
• Bank , R. E. and Rose , D. J. 1987 . Some error estimates for the box method . SIAM Journal on Numerical Analysis , 24 ( 4 ) : 777 – 787 .
   Web of Science ®Google Scholar
• Barth , T. 2004 . A taxonomy of consistently stabilized finite element methods for the stokes problem . SIAM Journal on Scientific and Statistical Computing , 25 : 1585 – 1607 .
   Web of Science ®Google Scholar
• Barth , W. L. and Carey , G. F. 2006 . On a natural convection benchmark problem in non-Newtonian fluids . Numerical Heat Transfer, Part B: Fundamentals , 50 ( 3 ) : 193 – 216 .
   Web of Science ®Google Scholar
• Behr , M. 2005 . “ GLS-type finite element methods for viscoelastic fluid flow simulation ” . In Proceedings of the Third MIT conference on computational fluid and solid dynamics , Edited by: Bathe , K. J. 586 – 589 . Cambridge, MA : Elsevier .
   Google Scholar
• Behr , M. A. , Franca , L. P. and Tezduyar , T. E. 1993 . Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows . Computer Methods in Applied Mechanics and Engineering , 104 : 31 – 48 .
   Web of Science ®Google Scholar
• Bochev , P. B. , Gunzburger , M. D. and Shadid , J. N. 2004 . Stability of the SUPG finite element method for transient advection-diffusion problems . Computer Methods in Applied Mechanics and Engineering , 193 : 2301 – 2323 .
   Web of Science ®Google Scholar
• Carey , G. F. 2004 . Modeling error and constitutive relations in simulation of flow and transport . International Journal for Numerical Methods in Fluids , 46 ( 12 ) : 1211 – 1236 .
   Web of Science ®Google Scholar
• Crumpton , P. I. and Shaw , G. J. 1992 . Cell vertex finite volume discretizations in three dimensions . International Journal for Numerical Methods in Fluids , 14 : 505 – 527 .
   Web of Science ®Google Scholar
• Delanaye , M. 1996 . Polynomial reconstruction finite volume schemes for the compressible Euler and Navier-Stokes equations on unstructured adaptive grids , Thesis PhD. University de Liege .
   Google Scholar
• Ebert , W. A. and Sparrow , E. M. 1965 . Slip flow in rectangular and annular ducts . Journal of Basic Engineering, Transactions of the ASME , 87 : 1018 – 1024 .
   Google Scholar
• Forsythe , J. R. 2002 . Detached eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow . Journal of Fluids Engineering , 124 ( 4 ) : 911 – 923 .
   Web of Science ®Google Scholar
• Gatlin , B. 1997 . Computation of converging and diverging flow through an asymmetric tubular bifurcation . ASME FEDSM97 , 3429 : 1 – 7 .
   Google Scholar
• Gelhard , T. 2005 . Stabilized finite element schemes with LBB-stable elements for incompressible flows . Journal of Computational and Applied Mathematics , 177 ( 2 ) : 243 – 267 .
   Web of Science ®Google Scholar
• Ghia , U. , Ghia , K. N. and Shin , C. T. 1982 . High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method . Journal of Computational Physics , 48 : 387 – 411 .
   Web of Science ®Google Scholar
• Girault , V. and Raviart , P. 1986 . Finite element methods for Navier-Stokes equations: theory and algorithms , Berlin : Springer .
   Google Scholar
• Guermond , J. L. , Minev , P. and Shen , J. 2006 . An overview of projection methods for incompressible flows . Computer Methods in Applied Mechanics and Engineering , 195 : 6011 – 6045 .
   Web of Science ®Google Scholar
• Gunzburger , M. D. 1989 . Finite element methods for viscous incompressible flows: theory, practice, and algorithms , San Diego : Academic Press .
   Google Scholar
• Herbin , R. 1995 . An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh . Numerical Methods for Partial Differential Equations , 11 ( 2 ) : 165 – 173 .
   Google Scholar
• Hermeline , F. A. 2000 . A finite volume method for the approximation of diffusion operators on distorted meshes . Journal of Computational Physics , 160 ( 2 ) : 481 – 499 .
   Web of Science ®Google Scholar
• Hettiarachchi , H. D.M. 2008 . Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature . International Journal of Heat and Mass Transfer , 51 : 5088 – 5096 .
   Web of Science ®Google Scholar
• Kapadia , S. , Roy , S. and Wurtzler , K. 2003 . Detached eddy simulation over a reference Ahmed car model In: 41st Aerospace Sciences Meeting and Exhibit, 6–9 January, Reno, NV, AIAA Paper No. 2003-0857
   Google Scholar
• Keyhani , M. and Kulacki , F. A. 1988 . Experiments on transient thermal convection with internal heating-large time results . ASME Journal of Heat Transfer , 5 ( 5 ) : 261 – 266 .
   Google Scholar
• Kulacki , F. A. and Emara , A. A. 1977 . Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources . Journal of Fluid Mechanics , 55 ( 2 ) : 271 – 287 .
   Web of Science ®Google Scholar
• Luo , H. , Baum , J. and Löhner , R. 1998 . A fast, matrix-free implicit method for compressible flows on unstructured grids . Journal of Computational Physics , 146 ( 2 ) : 664 – 690 .
   Web of Science ®Google Scholar
• Nikitin , N. V. 2000 . An approach to wall modeling in large-eddy simulations . Physics of Fluids , 12 ( 7 ) : 1629 – 1632 .
   Web of Science ®Google Scholar
• Renksizbulut , M. , Niazmand , H. and Tercan , G. 2006 . Slip-flow and heat transfer in rectangular microchannels with constant wall temperature . International Journal of Thermal Sciences , 45 : 870 – 881 .
   Web of Science ®Google Scholar
• Saad , Y. 1996 . Iterative methods for sparse linear systems , Boston, MA : PWS Publishing Company .
   Google Scholar
• Scott , A. M. 2003 . DES grid resolution issues for vertical flows on a Delta wing and an F–18C In: 41st Aerospace Sciences Meeting and Exhibit, 6–9 January, Reno, NV, AIAA Paper No. 2003-1103
   Google Scholar
• Shah , R. K. and London , A. L. 1978 . Laminar forced convection in ducts . Advances in Heat Transfer , : 196 – 222 . New York: Academic Press
   Google Scholar
• Spalart , P. R. Comments on the feasibility of LES for wings and on hybrid RANS/LES approach. Proceedings of the 1st AFOSR International Conference on DNS/LES . August 4–8 , Ruston, LA. Columbus, OH : Greyden Press .
   Google Scholar
• Strelets , M. 2001 . Detached eddy simulation of massively separated flows In: 39th AIAA Aerospace Sciences Meeting and Exhibit, 8–11 January, Reno, NV, AIAA Paper No. 2001-0879
   Google Scholar
• Timmermans , L. J.P. , Minev , P. D. and Van de Vosse , F. N. 1996 . An approximate projection scheme for incompressible flow using spectral elements . International Journal for Numerical Methods in Fluids , 22 ( 7 ) : 673 – 688 .
   Web of Science ®Google Scholar
• TRC . 1986 . Urban power plant plume studies Hill view Ave, Palo Alto, CA. EPRI Report EA–5468, Palo Alto, CA: EPRI, 3412
   Google Scholar
• Tu , S. and Aliabadi , S. 2007 . Development of a hybrid finite volume/element solver for incompressible flows on unstructured meshes . International Journal for Numerical Methods in Fluids , 55 ( 2 ) : 177 – 203 .
   Web of Science ®Google Scholar
• Tu , S. 2006 . Development and performance of CaMEL_Aero, a truly matrix-free, parallel, and vectorized unstructured finite volume solver for compressible flows In: Proceedings of the 25th Army Science Conference, 27–30 November, Orlando, FL
   Google Scholar
• Tu , S. 2009 . An implementation of the Spalart-Allmaras DES model in an implicit unstructured hybrid finite volume/element solver for incompressible turbulent flow . International Journal for Numerical Methods in Fluids , 59 ( 9 ) : 1051 – 1062 .
   Web of Science ®Google Scholar
• Visser , C. J. , Malan , A. G. and Meyer , J. P. 2008 . An artificial compressibility method for buoyancy-driven flow in heterogeneous saturated packed beds . International Journal of Numerical Methods for Heat & Fluid Flow , 18 : 900 – 918 .
   Web of Science ®Google Scholar
• Walters , K. and Luke , W. 3-D Navier-Stokes simulation of large-scale regions of the bronchopulmonary tree . Proceedings of IMECE . 13–19 November, Lake Buena Vista, FL, USA
   Google Scholar
• Wan , T. , Aliabadi , S. and Bigler , C. 2009 . A hybrid scheme based on finite element/volume methods for two immiscible fluid flows . International Journal for Numerical Methods in Fluids , 61 : 930 – 944 .
   Web of Science ®Google Scholar
• Warrell , D. 2003 . Oxford textbook of medicine-Vol 2 Oxford: Oxford University Press
   Google Scholar
• Yilmaz , E. 2007 . Urban CFD: extreme wind and air quality simulations for Indianapolis In: Indiana GIS Conference, 13–14 March, Indianapolis, IN, USA
   Google Scholar
• Yu , S. and Ameel , T. A. 2001 . Slip-flow heat transfer in rectangular microchannels. International . Journal of Heat and Mass Transfer , 44 : 4225 – 4234 .
   Web of Science ®Google Scholar
• Zhang , Z. and Kleinstreuer , C. 2003 . Species heat and mass transfer in a human upper airway model . International Journal of Heat and Mass Transfer , 46 : 4755 – 4768 .
   Web of Science ®Google Scholar