Numerical aspects of the simulation of discontinuous saline underflows: the lock-exchange problem

References

• Altinakar , M. S. , Graf , W. H. and Hopfinger , E. J. 1990 . Weakly depositing turbidity current on a small slope . J. Hydr. Res. , 28 ( 1 ) : 55 – 80 .
   Web of Science ®Google Scholar
• Altinakar , M. S. , Graf , W. H. and Hopfinger , E. J. 1996 . Flow structure in turbidity currents . J. Hydr. Res. , 34 ( 5 ) : 713 – 718 .
   Web of Science ®Google Scholar
• Alahyari , A. A. and Longmire , E. K. 1994 . Particle image velocimetry in a variable density flow: Application to a dynamically evolving microburst . Expts. Fluids , 17 : 434 – 440 .
   Web of Science ®Google Scholar
• Alahyari , A. A. and Longmire , E. K. 1996 . Development and structure of a gravity current head . Expts. Fluids , 20 : 410 – 416 .
   Web of Science ®Google Scholar
• Basombrïo , F. G. , Dari , E. A. , Buscaglia , G. C. and Feijoo , R. A. 2002 . Numerical experiments in complex hemodynamic flows: Non-Newtonian effects . Int. J. Comp. Fluid Dyn. , 16 ( 4 ) : 231 – 246 .
   Web of Science ®Google Scholar
• Bombardelli , F. A. and García , M. H. 2001 . “ Three-dimensional hydrodynamic modeling of density currents in the Chicago River, Illinois ” . In Civil Engineering Studies , Urbana-Champaign : Dept. of Civil and Environmental Eng., University of Illinois . Hydraulic Series 68
   Google Scholar
• Bombardelli , F. A. Characterization of coherent structures from parallel, LES computations of wandering effects in bubble plumes . Proc. World Water and Environmental Resources Congress . Edited by: Bizier , P. and DeBarry , P. Reston , , USA : Environmental & Water Resources Institute (EWRI), ASCE . CD-Rom
   Google Scholar
• Bombardelli , F. A. 2004 . Turbulence in multiphase models of aeration bubble plumes , Urbana , , USA : University of Illinois at Urbana-Champaign . Ph.D. Thesis
   Google Scholar
• Bournet , P. E. , Dartus , D. , Tassin , B. and Vincon-Leite , B. 1999 . Numerical investigation of plunging density currents . J. Hydr. Engng. , 125 ( 6 ) : 584 – 594 .
   Web of Science ®Google Scholar
• Bühler , J. , Wright , S. J. and Kim , Y. 1991 . Gravity currents advancing into a coflowing fluid . J. Hydr. Res. , 29 ( 2 ) : 243 – 257 .
   Web of Science ®Google Scholar
• Buscaglia , G. C. , Basombrío , F. G. and Codina , R. 2000 . Fourier analysis of an equal-order incompressible flow solver stabilized by pressure gradient projection . Int. J. Num. Meth. Fluids , 34 ( 1 ) : 65 – 92 .
   Web of Science ®Google Scholar
• Buscaglia , G. C. , Bombardelli , F. A. and García , M. H. 2002 . Numerical modeling of large-scale bubble plumes accounting for mass transfer effects . Int. J. Multiphase Flow , 28 : 1763 – 1785 .
   Web of Science ®Google Scholar
• Buscaglia , G. C. and Dari , E. A. 2003 . Numerical investigation of flow through a cavity with internal heat generation . Num. Heat Transfer A , 43 ( 5 ) : 525 – 541 .
   Web of Science ®Google Scholar
• Cantero , M. I. 2002 . Theoretical and numerical modeling of turbidity currents as a two-phase flow , Urbana , , USA : University of Illinois at Urbana-Champaign . M.S. Thesis
   Google Scholar
• Cantero , M. I. 2007 . Modeling and large scale simulations of thermohaline and particulate density currents , Urbana , , USA : University of Illinois at Urbana-Champaign . Ph.D. Thesis
   Google Scholar
• Cantero , M. I. , García , M. H. , Buscaglia , G. C. , Bombardelli , F. A. and Dari , E. A. Multidimensional CFD simulation of a discontinuous density current . Proc. 30 IAHR Congress, Water Engineering and Research in a Learning Society . Thessaloniki , Greece. Edited by: Ganoulis , J. and Prinos , P. CD-Rom
   Google Scholar
• Cantero , M. I. , Balachandar , S. , García , M. H. and Ferry , J. P. 2006 . Direct numerical simulations of planar and cylindrical density currents . J. Appl. Mech. Trans. ASME , 73 ( 6 ) : 923 – 930 .
   Web of Science ®Google Scholar
• Cantero , M. I. , Lee , J. R. , Balachandar , S. and García , M. H. 2007a . On the front velocity of gravity currents . J. Fluid Mech. , 586 : 1 – 39 .
   Web of Science ®Google Scholar
• Cantero , M. I. , Balachandar , S. and García , M. H. 2007b . High resolution simulations of cylindrical density currents . J. Fluid Mech. , 590 : 437 – 469 .
   Web of Science ®Google Scholar
• Cantero , M. I. , Balachandar , S. and García , M. H. 2008a . An Eulerian-Eulerian model for gravity currents driven by inertial particles . Int. J. Multiphase Flow , 34 ( 5 ) : 484 – 501 .
   Web of Science ®Google Scholar
• Cantero , M. I. , García , M. H. and Balachandar , S. 2008b . Effect of particle inertia on depositional particulate gravity currents . Comput. Geosci. , 34 ( 10 ) : 1307 – 1318 .
   Web of Science ®Google Scholar
• Cantero , M. I. , Balachandar , S. , García , M. H. and Bock , D. 2008c . Turbulent structures in planar gravity currents and their influence on the flow dynamics . J. Geophys. Res. Oceans , 113 ( C8 ) : C08018
   Web of Science ®Google Scholar
• Choi , S. U. and García , M. H. 1995 . Modelling of one-dimensional turbidity currents with a dissipative-Galerkin finite element method . J. Hydr. Res. , 33 ( 5 ) : 1 – 26 .
   Google Scholar
• Codina , R. 1993 . A discontinuity-capturing crosswind dissipation for the finite element solution of the convection diffusion equation . Comp. Meth. Appl. Mech. Engng. , 110 : 325 – 342 .
   Web of Science ®Google Scholar
• Codina , R. and Blasco , J. 1997 . A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation . Comp. Meth. Appl. Mech. Engng. , 143 : 373 – 391 .
   Web of Science ®Google Scholar
• Codina , R. and Blasco , J. 2000 . Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection . Comp. Meth. Appl. Mech. Engng. , 182 : 277 – 300 .
   Web of Science ®Google Scholar
• Constantinescu , G. S. , Ooi , S. K. and Weber , L. 2006 . Analysis of the evolution of finite-channel lock-release currents at high Grashof numbers from initial stages to the inviscid phase Edited by: Piasecki , M. Abstract published in Advances in HydroScience and Engineering
   Google Scholar
• Cortese , T. and Balachandar , S. 1995 . High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory . Int. J. Supercomput. Appl. , 9 ( 3 ) : 187 – 204 .
   Web of Science ®Google Scholar
• Crook , N. A. and Miller , M. J. 1985 . A numerical and analytical study of atmosphere undular bores . Quart. J. R. Met. Soc. , 111 : 225 – 242 .
   Web of Science ®Google Scholar
• Dallimore , C. J. , Imberger , J. and Hodges , B. R. 2004 . Modeling a plunging underflow . J. Hydr. Engng. , 130 ( 11 ) : 1068 – 1076 .
   Web of Science ®Google Scholar
• Daly , B. J. and Pratch , W. E. 1968 . Numerical study of density currents surges . Phys. Fluids , 11 : 15 – 30 .
   Web of Science ®Google Scholar
• De Cesare , G. , Schleiss , A. and Hermann , F. 2001 . Impact of turbidity currents on reservoir sedimentation . J. Hydr. Engng. , 127 ( 1 ) : 6 – 16 .
   Web of Science ®Google Scholar
• García , M. H. 1990 . Depositing and eroding sediment-driven flows: turbidity currents , Minneapolis , MN : St. Anthony Falls Hydraulic Lab., Univ. of Minnesota . Project Report 306
   Google Scholar
• García , M. H. and Parsons , J. D. 1996 . Mixing at the front of gravity currents . Dyn. Atm. Oceans , 24 : 197 – 205 .
   Web of Science ®Google Scholar
• Haase , S. P. and Smith , R. K. 1989 . The numerical simulation of atmospheric gravity currents 2: Environments with stable layers . Geophys. Astrophys. Fluid Dynamics , 46 : 35 – 51 .
   Web of Science ®Google Scholar
• Härtel , C. , Meiburg , E. and Necker , F. 2000 . Analysis and direct numerical simulation of the flow at a gravity current head 1: Flow topology and front speed for slip and no-slip boundaries . J. Fluid Mech. , 418 : 189 – 212 .
   Web of Science ®Google Scholar
• Huang , H. , Imran , J. and Pirmez , C. 2005 . Numerical model of turbidity currents with a deforming bottom boundary . J. Hydr. Engng. , 131 ( 4 ) : 283 – 293 .
   Web of Science ®Google Scholar
• Huang , H. , Imran , J. and Pirmez , C. 2007 . Numerical modeling of poorly sorted depositional turbidity currents . J. Geophys. Res. , 112 : C01014
   Web of Science ®Google Scholar
• Imran , J. , Kassem , A. and Khan , S. M. 2004 . Three-dimensional modeling of density current 1: Flow in a straight confined and unconfined channels . J. Hydr. Res. , 42 ( 6 ) : 578 – 590 .
   Web of Science ®Google Scholar
• Johnson , C. 1998 . Numerical solution of partial differential equations by the finite element method , NewYork , , USA : Cambridge University Press .
   Google Scholar
• Kassem , A. and Imran , J. 2004 . Three-dimensional modeling of density current 2: Flow in a sinuous confined and unconfined channels . J. Hydr. Res. , 42 ( 6 ) : 591 – 602 .
   Web of Science ®Google Scholar
• Khan , S. M. and Imran , J. 2008 . Numerical investigation of turbidity currents flowing through minibasins on the continental slope . J. Sedimentary Res. , 78 ( 3–4 ) : 245 – 257 .
   Web of Science ®Google Scholar
• Kundu , P. and Cohen , I. 2004 . Fluid mechanics, , 3rd ed. , San Diego , , USA : Elsevier .
   Google Scholar
• Leonard , B. P. and MacVean , M. K. 1995 . “ Grid refinement study of a benchmark problem using the flux-integral method ” . In Quantification of uncertainty in computational fluid dynamics , Edited by: Johnson , R. W. and Hughes , E. D. Vol. 213 , 45 – 50 . ASME-FED .
   Google Scholar
• Lew , A. , Buscaglia , G. C. and Carrica , P. 2001 . A note on the numerical treatment of the k-epsilon turbulence model . Int. J. Comput. Fluid Dyn. , 14 : 201 – 209 .
   Web of Science ®Google Scholar
• Marino , B. , Thomas , L. and Linden , P. 2005 . The front condition for gravity currents . J. Fluid Mech. , 536 : 49 – 78 .
   Web of Science ®Google Scholar
• Mitchell , K. E. and Hovermale , J. B. 1977 . A numerical investigation of a severe thunderstorm gust front . Monthly Weather Review , 105 : 657 – 675 .
   Web of Science ®Google Scholar
• Mueller , P. , Buscaglia , G. C. and Dari , E. A. Evaluation of a stabilized finite-element method for the simulation of homogeneous and isotropic turbulence . Proc. ENIEF, 13th Congress on Numerical methods and their applications . Bahia Blanca , Argentina. also Mecánica Computacional 22 (CD-Rom)
   Google Scholar
• Necker , F. , Hártel , C. , Kleiser , L. and Meiburg , E. 2002 . Highresolution simulations of particle-driven gravity currents . Int. J. Multiphase Flow , 28 : 279 – 300 .
   Web of Science ®Google Scholar
• Pacheco , J. R. , Pacheco-Vega , A. and Pacheco-Vega , S. 2000 . “ Numerical study of density currents using the non-staggered grid fractional step ” . In ASME Fluids Eng. Div. , 639 – 643 . NewYork : ASME .
   Google Scholar
• Parker , G. , García , M. H. , Fukushima , Y. and Yu , W. 1987 . Experiments on turbidity currents over an erodible bed . J. Hydr. Res. , 25 ( 1 ) : 123 – 147 .
   Web of Science ®Google Scholar
• Parsons , J. D. and García , M. H. 1998 . Similarity of gravity current fronts . Phys. Fluids , 10 ( 12 ) : 3209 – 3213 .
   Web of Science ®Google Scholar
• Roache , P. J. 1998 . Verification and validation in computational science and engineering , Socorro, NM , , USA : Hermosa Publishers .
   Google Scholar
• Sagaut , P. 2002 . Large eddy simulation for incompressible flows: An introduction , Berlin : Springer .
   Google Scholar
• Simpson , J. E. 1997 . Gravity currents , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Straka , J. M. , Wilhelmson , R. B. , Wicker , L. J. , Anderson , J. R. and Droegemeier , K. K. 1993 . Numerical solutions of a non-linear density current: a benchmark solution and comparisons . Int. J. Num. Meth. Fluids , 17 : 1 – 22 .
   Web of Science ®Google Scholar
• Thorpe , A. J. , Miller , M. J. and Moncrieff , M. W. 1980 . Dynamical models of two-dimensional downdraughts . Quart. J. R. Met. Soc. , 106 : 463 – 484 .
   Web of Science ®Google Scholar
• Xue , M. , Xu , Q. and Droegemeier , K. K. 1997 . A theoretical and numerical study of density currents in non-constant shear flows . J. Atmos. Sci. , 54 : 1998 – 2019 .
   Web of Science ®Google Scholar
• Wilcox , D. C. 1993 . Turbulence modeling for CFD La Ca˜ada, Valley Sun, CA , , USA
   Google Scholar