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Moes, N.1999-Hierarchical modeling of heterogeneous solids3-255Computer Methods in Applied Mechanics and Engineering1721-4Apr://000080052800002 ISI:000080052800002D?"Braatz, R. D. He, Y. Alkire, R. C.20058Guidelines for the Design of Multiscale Simulation Codes2005 AIChE Annual MeetingCincinnati, Ohio9http://aiche.confex.com/aiche/2005/techprogram/P30721.HTM?2Woo, X. Y. Tan, R. B. H. Chow, P. S. Braatz, R. D.2006`Simulation of mixing effects in antisolvent crystallization usingI a coupled CFD-PDF-PBE approach 1291-1303Crystal Growth & Design6}?Vlachos, D. G.1999ZThe role of macroscopic transport phenomena in film microstructure during epitaxial growth 2797-2799Applied Physics Letters7419May://000080152700021 0003-6951ISI:000080152700021}?Vlachos, D. G.1997OMultiscale integration hybrid algorithms for homogeneous-heterogeneous reactors 3031-3041 Aiche Journal4311Nov://A1997YF72500014 0001-1541ISI:A1997YF72500014}?*Lipatov, A. S. Motschmann, U. Bagdonat, T.2002L3D hybrid simulations of the interaction of the solar wind with a weak comet403-411Planetary and Space Science504Apr://000176453800007 0032-0633ISI:000176453800007F|?6De Fabritiis, G. Delgado-Buscalioni, R. Coveney, P. V.20069Multiscale modeling of liquids with molecular specificityPhysical Review Letters9713Sep://000240872700026 134501 0031-9007ISI:000240872700026+}?6Li, J. Kevrekidis, P. G. Gear, C. W. Kevrekidis, I. G.2003eDeciding the nature of the coarse equation through microscopic simulations: The baby-bathwater scheme391-407 Multiscale Modeling & Simulation13://000221348400003 1540-3459ISI:000221348400003}?9Garcia, A. L. Bell, J. B. Crutchfield, W. Y. Alder, B. J.1999JAdaptive mesh and algorithm refinement using direct simulation Monte Carlo134-155 Journal of Computational Physics1541Sep://000082430200006 0021-9991ISI:000082430200006}?)Hornung, R. D. Wissink, A. M. Kohn, S. R.2006JManaging complex data and geometry in parallel structured AMR applications181-195Engineering with Computers223-4://000243365500004 0177-0667ISI:000243365500004}?#Schwartzentruber, T. E. Boyd, I. D.20069A hybrid particle-continuum method applied to shock waves402-416 Journal of Computational Physics2152Jul://000237458200003 0021-9991ISI:000237458200003}?Tello, J. S. Curtin, W. A.2005;A coupled discrete/continuum model for multiscale diffusion257-265>International Journal for Multiscale Computational Engineering33://000235550200001 1543-1649ISI:000235550200001C}?\Kolobov, V. I. Bayyuk, S. A. Arslanbekov, R. R. Aristov, V. V. Frolova, A. A. Zabelok, S. A.2005KConstruction of a unified continuum/kinetic solver for aerodynamic problems598-606!Journal of Spacecraft and Rockets424Jul-Aug://000231136900003 0022-4650ISI:000231136900003J}?GWijesinghe, H. S. Hornung, R. D. Garcia, A. L. Hadjiconstantinou, N. G.2004UThree-dimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics768-7776Journal of Fluids Engineering-Transactions of the Asme1265Sep://000225805500009 0098-2202ISI:000225805500009F|?Hadjiconstantinou, N. G.2004DCombining atomistic and continuum simulations of contact-line motionPhysical Review E696Jun://000222502800149 Part 2 069901 1063-651XISI:000222502800149$}?*Wijesinghe, H. S. Hadjiconstantinou, N. G.2004TA hybrid atomistic-continuum formulation for unsteady, viscous, incompressible flows515-5260Cmes-Computer Modeling in Engineering & Sciences56Jun://000222301300003 1526-1492ISI:000222301300003}?(Attinger, S. Micha, J. D. Kinzelbach, W.2003=Multiscale modeling of nonlinearly adsorbing solute transport408-431 Multiscale Modeling & Simulation13://000221348400004 1540-3459ISI:000221348400004}?Niessner, J. Helmig, R.2006XMulti-scale modelling of two-phase-two-component processes in heterogeneous porous media699-715*Numerical Linear Algebra with Applications139Nov://000241957900003 1070-5325ISI:000241957900003}?Ming, P. B. Zhang, P. W.2006UAnalysis of the heterogeneous multiscale method for parabolic homogenization problems153-177Mathematics of Computation76257://000241791500008 0025-5718ISI:000241791500008 }?!Rabczuk, T. Xiao, S. P. Sauer, A.2006SCoupling of mesh-free methods with finite elements: basic concepts and test results 1031-10652Communications in Numerical Methods in Engineering2210Oct://000241049300002 1069-8299ISI:000241049300002 F|? E, W. Liu, D. Vanden-Eijnden, E.2005XNested stochastic simulation algorithm for chemical kinetic systems with disparate ratesJournal of Chemical Physics12319Nov://000233353200007 194107 0021-9606ISI:000233353200007F|?To, A. C. Li, S. F.2005(Perfectly matched multiscale simulationsPhysical Review B723Jul://000230890200158 035414 1098-0121ISI:000230890200158#}?Chen, S. Q. E, W. N. Shu, C. W.2005tThe heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems871-894 Multiscale Modeling & Simulation34://000229826400009 1540-3459ISI:000229826400009F|?"Choly, N. Lu, G. E, W. Kaxiras, E.2005OMultiscale simulations in simple metals: A density-functional-based methodologyPhysical Review B719Mar://000228727100030 094101 1098-0121ISI:000228727100030}? Chai, L. H.2005%Recent progress of multiscale science186-191Progress in Chemistry172Mar://000228073500002 1005-281XISI:000228073500002 }?.Nie, X. B. Chen, S. Y. E, W. N. Robbins, M. O.2004OA continuum and molecular dynamics hybrid method for micro- and nano-fluid flow55-64Journal of Fluid Mechanics500Feb://000220638800003 0022-1120ISI:000220638800003}?E, W. N. Ming, P. B.2004Analysis of multiscale methods210-219$Journal of Computational Mathematics222Mar://000220381000008 0254-9409ISI:000220381000008}?Wagner, G. J. Liu, W. K.2003TCoupling of atomistic and continuum simulations using a bridging scale decomposition249-274 Journal of Computational Physics1901Sep://000220234800013 0021-9991ISI:000220234800013F|?E, W. Engquist, B. Huang, Z. Y.2003NHeterogeneous multiscale method: A general methodology for multiscale modelingPhysical Review B679Mar://000182019300001 092101 1098-0121ISI:000182019300001}?Li, J. H. Kwauk, M.2003OExploring complex systems in chemical engineering - the multi-scale methodology521-535Chemical Engineering Science583-6Feb-Mar://000181575600002 0009-2509ISI:000181575600002}?Martys, N. S. Hagedorn, J. G.2002bMultiscale modeling of fluid transport in heterogeneous materials using discrete Boltzmann methods650-658Materials and Structures35254Dec://000180564100008 1359-5997ISI:000180564100008 }?/Jendrejack, R. M. de Pablo, J. J. Graham, M. D.2002<A method for multiscale simulation of flowing complex fluids123-142(Journal of Non-Newtonian Fluid Mechanics1081-3Dec://000180381900007 0377-0257ISI:000180381900007}?Raimondeau, S. Vlachos, D. G.2002MRecent developments on multiscale, hierarchical modeling of chemical reactors3-23Chemical Engineering Journal901-2Nov://000179225400002 1385-8947ISI:000179225400002E}?1De Fabritiis, G. D. Coveney, P. V. Flekkoy, E. G.2002(Multiscale dissipative particle dynamics317-331qPhilosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences3601792Mar://000174649600005 1364-503XISI:000174649600005F|?E, W. N. Huang, Z. Y.2001@Matching conditions in atomistic-continuum modeling of materialsPhysical Review Letters871313Sep://000171219500032 135501 0031-9007ISI:000171219500032Yneering672Jul://000239030500007 0029-5981ISI:000239030500007 }?!Tang, S. Q. Hou, T. Y. Liu, W. 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Koumoutsakos, P.2006RA software framework for the portable parallelization of particle-mesh simulations730-739!Euro-Par 2006 Parallel Processing4128://000241469500066 !Lecture Notes in Computer Science 0302-9743ISI:000241469500066 }?*Werder, T. Walther, J. H. Koumoutsakos, P.2005IHybrid atomistic-continuum method for the simulation of dense fluid flows373-390 Journal of Computational Physics2051May://000228707100018 0021-9991ISI:000228707100018}?Ren, W. Q. E, W.2005UHeterogeneous multiscale method for the modeling of complex fluids and micro-fluidics1-26 Journal of Computational Physics2041Mar://000227733600001 0021-9991ISI:000227733600001}?Koumoutsakos, P.2005+Multiscale flow simulations using particles457-487 Annual Review of Fluid Mechanics37://000226822300018 0066-4189ISI:000226822300018 }?*Ingram, G. D. Cameron, I. T. Hangos, K. 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Meakin, P.2008RMixing-induced precipitation: Experimental study and multiscale numerical analysisWater Resources Research446dSMOOTHED PARTICLE HYDROD xomputational PhysicsF|?Moro, E.2004LHybrid method for simulating front propagation in reaction-diffusion systemsPhysical Review E696Jun://000222502700001 Part 1 060101 1063-651XISI:000222502700001}?Curtin, W. A. Miller, R. E.2003?Atomistic/continuum coupling in computational materials scienceR33-R68=Modelling and Simulation in Materials Science and Engineering113May://000183137700001 0965-0393ISI:000183137700001|?#Flekkoy, E. G. Feder, J. Wagner, G.20019Coupling particles and fields in a diffusive hybrid model066302Physical Review E646Dec://000172726400047 Part 2 066302 1063-651XISI}?Efendiev, Y. Durlofsky, L. J.2003NA generalized convection-diffusion model for subgrid transport in porous media504-526 Multiscale Modeling & Simulation13://000221348400008 1540-3459ISI:000221348400008}?E, W. Huang, Z. 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A.2004ZAdaptive multiscale finite-volume method for multiphase flow and transport in porous media50-64 Multiscale Modeling & Simulation31://000227305700003 1540-3459ISI:000227305700003}?!Kroger, M. Stankovic, I. Hess, S.2003OTowards multiscale modeling of metals via embedded particle computer simulation25-39 Multiscale Modeling & Simulation11://000221320700002 1540-3459ISI:000221320700002}?Sun, Y. Engquist, B.2006LHeterogeneous multiscale methods for interface tracking of combustion fronts532-563 Multiscale Modeling & Simulation52://000240432000009 1540-3459ISI:000240432000009}?Tartakovsky, A. M. Meakin, P.2006`Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics 1464-1478Advances in Water Resources2910Oct://000241257400004 0309-1708ISI:000241257400004F|?Tartakovsky, A. Meakin, P.2005SModeling of surface tension and contact angles with smoothed particle hydrodynamicsPhysical Review E722Aug://000231564100082 Part 2 026301 1539-3755ISI:000231564100082}?Tartakovsky, A. M. Meakin, P.2005YSimulation of unsaturated flow in complex fractures using smoothed particle hydrodynamics848-855Vadose Zone Journal43Aug://000231358400027 1539-1663ISI:000231358400027A}?Tartakovsky, A. M. Meakin, P.2005A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh-Taylor instability610-624 Journal of Computational Physics2072Aug://000229711100010 0021-9991ISI:000229711100010}?Xiu, D. B. Kevrekidis, I. G.2005CEquation-free, multiscale computation for unsteady random diffusion915-935 Multiscale Modeling & Simulation43://000232354400009 1540-3459ISI:000232354400009}?;Sirisup, S. Karniadakis, G. E. Xiu, D. B. Kevrekidis, I. G.2005LEquation-free/Galerkin-free POD-assisted computation of incompressible flows568-587 Journal of Computational Physics2072Aug://000229711100008 0021-9991ISI:000229711100008}?'Xiu, D. B. Kevrekidis, I. G. Ghanem, R.2005CAn equation-free, multiscale approach to uncertainty quantification16-23"Computing in Science & Engineering73May-Jun://000228487100005 1521-9615ISI:000228487100005}?#Tartakovsky, D. M. Alexander, F. J.20053Multiphysics modeling - Guest editors' introduction14-15"Computing in Science & Engineering73May-Jun://000228487100004 1521-9615ISI:000228487100004 }?5Martin, D. F. Colella, P. Anghel, M. Alexander, F. J.2005>Adaptive mesh refinement for multiscale nonequilibrium physics24-31"Computing in Science & Engineering73May-Jun://000228487100006 1521-9615ISI:000228487100006}?1Alexander, F. J. Tartakovsky, D. M. Garcia, A. L.2005%Noise in algorithm refinement methods32-38"Computing in Science & Engineering73May-Jun://000228487100007 1521-9615ISI:000228487100007}?-Symeonidis, V. Karniadakis, G. E. Caswell, B.2005:A seamless approach to multiscale complex fluid simulation39-46"Computing in Science & Engineering73May-Jun://000228487100008 1521-9615ISI:000228487100008}? Hyman, J. M.2005&Patch dynamics for multiscale problems47-53"Computing in Science & Engineering73May-Jun://000228487100009 1521-9615ISI:000228487100009}?O'Leary, D. P.2005;Finite differences and finite elements: Getting to know you72-75"Computing in Science & Engineering73May-Jun://000228487100013 1521-9615ISI:000228487100013}? Dubois, P. F.2005.Maintaining correctness in scientific programs80-85"Computing in Science & Engineering73May-Jun://000228487100015 1521-9615ISI:000228487100015 $h finite elements 1448-1458Computers & Structures8317-18Jun://000230160600007 0045-7949ISI:000230160600007;<}?Wang, C. Y. Zhang, X.20061Multiscale modically spanning the length scales from the quantum to the continuum 1135-1148)International Journal of Modern Physics C116Sep://000166141900006 0129-1831ISI:000166141900006}?9Abraham, F. F. Broughton, J. Q. Bernstein, N. Kaxiras, E.19980Spanning the length scales in dynamic simulation538-546Computers in Physics126Nov-Dec://000077611900013 0894-1866ISI:000077611900013Gp}?!Kojic, M. Filipovic, N. Tsuda, A.2007}A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method821-8335Computer Methods in Applied Mechanics and Engineering1976-}?9Csanyi, G. Albaret, T. Moras, G. Payne, M. C. De Vita, A.20059Multiscale hybrid simulation methods for material systems R691-R703#Journal of Physics-Condensed Matter1727Jul://000231003900003 0953-8984ISI:000231003900003 2222F??Tartakovsky, A. M. Tartakovsky, D. M. Scheibe, T. D. 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Yotov, I.2007/A multiscale mort ar mixed finite element method319-346 Multiscale Modeling & Simulation61://000246923200016 1540-3459ISI:000246923200016$|?Bernholdt, D. E.2007^Special issue: Component and framework technology in high-performance and scientific computing571-5721Concurrency and Computation-Practice & Experience195Apr://000245572300001 Sp. Iss. SI 1532-0626ISI:000245572300001R}?YAllan, B. A. Armstrong, R. Bernholdt, D. E. Bertrand, F. Chiu, K. Dahlgren, T. L. Damevski, K. Elwasif, W. R. Epperly, T. G. W. Govindaraju, M. Katz, D. S. Kohl, J. A. Krishnan, M. Kumfert, G. Larson, J. W. Lefantzi, S. Lewis, M. J. Malony, A. D. McInnes, L. C. Nieplocha, J. Norris, B. Parker, S. G. Ray, J. Shende, S. Windus, T. L. Zhou, S. J.2006BA component architecture for high-performance scientific computing163-202@International Journal of High Performance Computing Applications202Sum://000238259800002 1094-3420ISI:000238259800002-?@Karpov, E. G. Yu, H. Park, H. S. Liu, W. K. Wang, Q. J. Qian, D.2006_Multiscale boundary conditions in crystalline solids: Theory and application to nanoindentation 6359-6379.International Journal of Solids and Structures431Ilenia is basing here initial work on this paper. :000172726400047|? O'Connell, S. T. Thompson, P. A.1995YMolecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows R5792-R5795Physical Review E526Dec://A1995TK6 35300018 Part A 1063-651XISI:A1995TK65300018 D}?Li, J. Liao, D. Y. Yip, S.1998gCoupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator 7259-7267Physical Review E576Jun://000074252400129 1063-651XISI :000074252400129+}?HLiu, W. K. Park, H. S. Qian, D. Karpov, E. G. Kadowaki, H. Wagner, G. J.20066Bridging scale methods for nanomechanics and materials 1407-14215Computer Methods in Applied Mechanics and Engineering19513-16://000235438000006 0045-7825ISI:000235438000006}?.Liu, W. K. Karpov, E. G. Zhang, S. Park, H. S.2004<An introduction to computational nanomechanics and materials 1529-15785Computer Methods in Applied Mechanics and Engineering19317-20://000220968900002 0045-7825ISI:000220968900002}?:E, W. Engquist, B. Li, X. T. Ren, W. Q. Vanden-Eijnden, E.2007*Heterogeneous multiscale methods: A review367-450'Communications in Computational Physics23Jun://000246378800001 1815-2406ISI:000246378800001_͌}?)Fernandez-Mendez, S. Bonet, J. Huerta, A.2005/Continuous blending of SPH wit }?-Attaway, S. W. Heinstein, M. W. Swegle, J. W.1994HCoupling of Smooth Particle Hydrodynamics with the Finite-Element Method199-205Nuclear Engineering and Design1502-3Sep://A1994PN87800002 0029-5493ISI:A1994PN87800002}?*De Vuyst, T. Vignjevic, R. Campbell, J. C.20054Coupling between meshless and finite element methods 1054-1064+International Journal of Impact Engineering318Sep://000228036000008 0734-743XISI:000228036000008}?2Brown, K. Attaway, S. Plimpton, S. Hendrickson, B.20004Parallel strategies for crash and impact simulations375-3905Computer Methods in Applied Mechanics and Engineering1842-4://000086400400010 0045-7825ISI:000086400400010&}?*Huerta, A. Fernandez-Mendez, S. Liu, W. K.2004OA comparison of two formulations to blend finite elements and mesh-free methods 1105-11175Computer Methods in Applied Mechanics and Engineering19312-14://000220555400009 0045-7825ISI:000220555400009}?*Johnson, G. R. Stryk, R. A. Beissel, S. R.1996)SPH for high velocity impact computations347-3735Computer Methods in Applied Mechanics and Engineering1391-4Dec://A1996WA55800013 0045-7825ISI:A1996WA55800013|? Weimar, J. R.20016Coupling microscopic and macroscopic cellular automata601-611Parallel Computing275Apr://000167975200006 Sp. Iss. SI 0167-8191ISI:000167975200006 LF://000246851000001 W05437 0043-1397ISI:000246851000001ISI:000252042300024 D8://000251657100025 0045-7825ISI:000251657100025? Morris, J. P. Fox, P. J. Zhu, Y.1997< Modeling low Reynolds number incompressible flows using SPH214-226 Journal of Computational Physics136 YNAMICS; POROUS-MEDIA; REACTIVE TRANSPORT; MODEL; DIFFUSION; FLOW; FRACTURESArticleJunLaboratory experiments, pore-scale simulations, and continuum (Darcy) -scale simulations were used to study mixing-induced precipitation in porous media. In the experimental investigation, solutions containing Na2CO3 and CaCl2 were each injected in different halves of a quasi two-dimensional flow cell filled with quartz sand. As a result of the in situ mixing between the two solutions, a narrow calcite precipitate layer (less than 5 mm wide) of more or less uniform width was formed between the individual solutions. Pore-scale simulations were conducted to help understand the mechanism of precipitation layer formation. The effect of the Peclet number, Pe, and the Damkohler number, Da, on mixing induced precipitation was also investigated. Pore-scale simulations revealed the presence of large pore-scale concentration gradients. This, and the presence of features, such as the precipitation layer, with characteristic lengths on the order of the average sand grain diameter, indicate the absence of a clear scale separation required for the strict derivation of Darcy-scale advection-dispersion equations. Nevertheless, we found that an adaptive high-resolution model based on advection-dispersion equations with grid sizes in the mixing zone smaller than the size of the sand grains can qualitatively reproduce the essential features of the experiment. As an alternative to computationally expensive high-resolution simulations, we proposed new forms for the homogeneous and heterogeneous reaction terms in Darcy-scale advection dispersion equations. These terms involve transport and mixing indices that account for highly nonuniform pore-scale concentration distributions and highly localized reactions. The proposed model accurately estimates the changes in solute concentrations due to homogenous and heterogeneous reactions during precipitation of minerals, observed in the pore-scale simulations, while conventional low-resolution advective-dispersion equations produced erroneous results.://000257317200001 PISI Document Delivery No.: 321OV Times Cited: 0 Cited Reference Count: 24 W06S04 0043-1397Water Resour. Res.ISI:000257317200001Pacific NW Natl Lab, Richland, WA 99352 USA. Idaho Natl Lab, Idaho Falls, ID 83415 USA. Los Alamos Natl Lab, Los Alamos, NM 87545 USA. Tartakovsky, AM, Pacific NW Natl Lab, POB 999, Richland, WA 99352 USA. alexandre.tartakovsky@pnl.gov