A Comprehensive Review of Recent Advances in Scalar Convection- Diffusion Studies

Authors

  • Aslam Abdullah Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia
  • Siti Nur Mariani Mohd Yunos Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia
  • Bambang Basuno Mechanical Engineering Department, Faculty of Engineering, Universitas Muhammadiyah Surakarta, Jl. A. Yani, Pabelan, Kartasura, Sukoharjo, Jawa Tengah, 57169, Indonesia

DOI:

https://doi.org/10.37934/arnht.27.1.1427

Keywords:

Convection-diffusion, Transport properties, Theoretical perspective, Extracellular perspective, Chemical reaction, Turbulence, Diffusivity, Mixing

Abstract

Scalar convection-diffusion has been drawing attention in fluid mechanics since more than half a century due to its relevance in various applications, its impact on transport properties, and its interplay with other fluid phenomena. In this review, we summarize the recent advances in scalar convection-diffusion studies documented by various researchers in efforts to identify an appropriate case study for using the model of convection-diffusion correctly. Scalar convection-diffusion studies are classified as theoretical, numerical solution, extracellular, chemical reaction, turbulence, diffusivity, and mixing perspectives since different perspectives have their own context. This paper has examined and articulated a range of viewpoints with different emphases. Encapsulating the latest advancements in the study of scalar convection-diffusion processes for future case study applications is the goal of this review.

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Author Biographies

Aslam Abdullah, Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia

aslam@uthm.edu.my

Siti Nur Mariani Mohd Yunos, Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia

nmariani@uthm.edu.my

Bambang Basuno, Mechanical Engineering Department, Faculty of Engineering, Universitas Muhammadiyah Surakarta, Jl. A. Yani, Pabelan, Kartasura, Sukoharjo, Jawa Tengah, 57169, Indonesia

basunobambang117@gmail.com

References

Yang, Yantao, Roberto Verzicco, and Detlef Lohse. "Two-scalar turbulent Rayleigh–Bénard convection: numerical simulations and unifying theory." Journal of fluid mechanics 848 (2018): 648-659. https://doi.org/10.1017/jfm.2018.378 DOI: https://doi.org/10.1017/jfm.2018.378

Long, Zichao, Yiping Lu, Xianzhong Ma, and Bin Dong. "PDE-NET: Learning PDEs from data." In International conference on machine learning, pp. 3208-3216. PMLR, 2018. https://doi.org/10.48550/arxiv.1710.09668

Feistauer, Miloslav and Václav Kučera. "On a robust discontinuous Galerkin technique for the solution of compressible flow." Journal of Computational Physics 224, no. 1 (2007): 208-221. https://doi.org/10.1016/j.jcp.2007.01.035 DOI: https://doi.org/10.1016/j.jcp.2007.01.035

Jin, Byung-Ju, Alex J. Smith, and Alan S. Verkman. "Spatial model of convective solute transport in brain extracellular space does not support a “glymphatic” mechanism." Journal of General Physiology 148, no. 6 (2016): 489-501. https://doi.org/10.1085/jgp.201611684 DOI: https://doi.org/10.1085/jgp.201611684

Almarcha, Christophe, Philip M.J. Trevelyan, Patrick Grosfils, and Anne De Wit. "Chemically driven hydrodynamic instabilities." Physical review letters 104, no. 4 (2010): 044501. https://doi.org/10.1103/physrevlett.104.044501 DOI: https://doi.org/10.1103/PhysRevLett.104.044501

Kerstein, Alan R. "Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential molecular diffusion in round jets." Journal of Fluid Mechanics 216 (1990): 411-435. https://doi.org/10.1017/s0022112090000489 DOI: https://doi.org/10.1017/S0022112090000489

Yang, Yantao, Roberto Verzicco, and Detlef Lohse. "From convection rolls to finger convection in double-diffusive turbulence." Proceedings of the National Academy of Sciences 113, no. 1 (2016): 69-73. https://doi.org/10.1073/pnas.1518040113 DOI: https://doi.org/10.1073/pnas.1518040113

Yang, Yantao, Roberto Verzicco, Detlef Lohse, and C. P. Caulfield. "Layering and vertical transport in sheared double-diffusive convection in the diffusive regime." Journal of fluid mechanics 933 (2022): A30. https://doi.org/10.1017/jfm.2021.1091 DOI: https://doi.org/10.1017/jfm.2021.1091

Wane, B. A., J. M. Urquiza, A. Fortin, and D. Pelletier. "Hierarchical elements for the iterative solving of turbulent flow problems on anisotropic meshes." European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique 21, no. 1-2 (2012): 22-39. https://doi.org/10.13052/17797179.2012.702428 DOI: https://doi.org/10.1080/17797179.2012.702428

Winters, Kraig B. and Eric A. D'Asaro. "Diascalar flux and the rate of fluid mixing." Journal of Fluid Mechanics 317 (1996): 179-193. https://doi.org/10.1017/s0022112096000717 DOI: https://doi.org/10.1017/S0022112096000717

Grossmann, Siegfried and Detlef Lohse. "Thermal convection for large Prandtl numbers." Physical review letters 86, no. 15 (2001): 3316. https://doi.org/10.1103/physrevlett.86.3316 DOI: https://doi.org/10.1103/PhysRevLett.86.3316

Stevens, Richard JAM, Erwin P. van der Poel, Siegfried Grossmann, and Detlef Lohse. "The unifying theory of scaling in thermal convection: the updated prefactors." Journal of fluid mechanics 730 (2013): 295-308. https://doi.org/10.1017/jfm.2013.298 DOI: https://doi.org/10.1017/jfm.2013.298

Ng, Chong Shen, Andrew Ooi, Detlef Lohse, and Daniel Chung. "Vertical natural convection: application of the unifying theory of thermal convection." Journal of Fluid Mechanics 764 (2015): 349-361. https://doi.org/10.1017/jfm.2014.712 DOI: https://doi.org/10.1017/jfm.2014.712

Schmidt, Laura E., Enrico Calzavarini, Detlef Lohse, Federico Toschi, and Roberto Verzicco. "Axially homogeneous Rayleigh–Bénard convection in a cylindrical cell." Journal of fluid mechanics 691 (2012): 52-68. https://doi.org/10.1017/jfm.2011.440 DOI: https://doi.org/10.1017/jfm.2011.440

Du, Yuhang, Mengqi Zhang, and Yantao Yang. "Two-component convection flow driven by a heat-releasing concentration field." Journal of Fluid Mechanics 929 (2021): A35. https://doi.org/10.1017/jfm.2021.715 DOI: https://doi.org/10.1017/jfm.2021.715

Wang, Qi, Detlef Lohse, and Olga Shishkina. "Scaling in internally heated convection: a unifying theory." Geophysical research letters 48, no. 4 (2021): e2020GL091198. https://doi.org/10.1029/2020gl091198 DOI: https://doi.org/10.1029/2020GL091198

Jones, Chris A., Krzysztof A. Mizerski, and Mouloud Kessar. "Fully developed anelastic convection with no-slip boundaries." Journal of Fluid Mechanics 930 (2022): A13. https://doi.org/10.1017/jfm.2021.905 DOI: https://doi.org/10.1017/jfm.2021.905

Georgoulis, Emmanuil H., Edward Hall, and Jens Markus Melenk. "On the suboptimality of the p-version interior penalty discontinuous Galerkin method." Journal of Scientific Computing 42 (2010): 54-67. https://doi.org/10.1007/s10915-009-9315-z DOI: https://doi.org/10.1007/s10915-009-9315-z

Brdar, Slavko, Andreas Dedner, and Robert Klöfkorn. "Compact and stable Discontinuous Galerkin methods for convection-diffusion problems." SIAM Journal on Scientific Computing 34, no. 1 (2012): A263-A282. https://doi.org/10.1137/100817528 DOI: https://doi.org/10.1137/100817528

Busto, Saray, Maurizio Tavelli, Walter Boscheri, and Michael Dumbser. "Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems." Computers & Fluids 198 (2020): 104399. https://doi.org/10.1016/j.compfluid.2019.104399 DOI: https://doi.org/10.1016/j.compfluid.2019.104399

Hundsdorfer, Willem. "Partially implicit BDF2 blends for convection dominated flows." SIAM journal on numerical analysis 38, no. 6 (2001): 1763-1783. https://doi.org/10.1137/s0036142999364741 DOI: https://doi.org/10.1137/S0036142999364741

Schütz, Jochen, and Vadym Aizinger. "A hierarchical scale separation approach for the hybridized discontinuous Galerkin method." Journal of Computational and Applied Mathematics 317 (2017): 500-509. https://doi.org/10.1016/j.cam.2016.12.018 DOI: https://doi.org/10.1016/j.cam.2016.12.018

Ding, Mingchang, Xiaofeng Cai, Wei Guo, and Jing-Mei Qiu. "A semi-Lagrangian discontinuous Galerkin (DG)–local DG method for solving convection-diffusion equations." Journal of Computational Physics 409 (2020): 109295. https://doi.org/10.1016/j.jcp.2020.109295 DOI: https://doi.org/10.1016/j.jcp.2020.109295

Albi, Giacomo, and Lorenzo Pareschi. "High Order Semi-Implicit Multistep Methods for Time-Dependent Partial Differential Equations." Communications on Applied Mathematics and Computation 3 (2021): 701-718. https://doi.org/10.48550/arxiv.2001.03974 DOI: https://doi.org/10.1007/s42967-020-00110-5

Ioriatti, Matteo, Michael Dumbser, and Raphaël Loubère. "A staggered semi-implicit discontinuous galerkin scheme with a posteriori subcell finite volume limiter for the euler equations of gasdynamics." Journal of Scientific Computing 83, no. 2 (2020): 27. https://doi.org/10.1007/s10915-020-01209-w DOI: https://doi.org/10.1007/s10915-020-01209-w

Badia, Santiago, Jesús Bonilla, and Alba Hierro. "Differentiable monotonicity-preserving schemes for discontinuous Galerkin methods on arbitrary meshes." Computer Methods in Applied Mechanics and Engineering 320 (2017): 582-605. https://doi.org/10.1016/j.cma.2017.03.032 DOI: https://doi.org/10.1016/j.cma.2017.03.032

Smith, Alex J., and Alan S. Verkman. "The “glymphatic” mechanism for solute clearance in Alzheimer’s disease: game changer or unproven speculation?" The FASEB Journal 32, no. 2 (2018): 543. https://doi.org/10.1096/fj.201700999 DOI: https://doi.org/10.1096/fj.201700999

Ray, Lori, Jeffrey J. Iliff, and Jeffrey J. Heys. "Analysis of convective and diffusive transport in the brain interstitium." Fluids and Barriers of the CNS 16, no. 1 (2019): 1-18. https://doi.org/10.1186/s12987-019-0126-9 DOI: https://doi.org/10.1186/s12987-019-0126-9

Wolak, Daniel J., Michelle E. Pizzo, and Robert G. Thorne. "Probing the extracellular diffusion of antibodies in brain using in vivo integrative optical imaging and ex vivo fluorescence imaging." Journal of Controlled Release 197 (2015): 78-86. https://doi.org/10.1016/j.jconrel.2014.10.034 DOI: https://doi.org/10.1016/j.jconrel.2014.10.034

Abbott, N. Joan, Michelle E. Pizzo, Jane E. Preston, Damir Janigro, and Robert G. Thorne. "The role of brain barriers in fluid movement in the CNS: is there a ‘glymphatic’system?." Acta neuropathologica 135 (2018): 387-407. https://doi.org/10.1007/s00401-018-1812-4 DOI: https://doi.org/10.1007/s00401-018-1812-4

Walker, Wynn L., and Julian Cook. "Drug delivery to brain tumors." Bulletin of mathematical biology 58 (1996): 1047-1074. https://doi.org/10.1016/s0092-8240(96)00025-0 DOI: https://doi.org/10.1016/S0092-8240(96)00025-0

Smith, Alex J., Xiaoming Yao, James A. Dix, Byung-Ju Jin, and Alan S. Verkman. "Test of the'glymphatic'hypothesis demonstrates diffusive and aquaporin-4-independent solute transport in rodent brain parenchyma." elife 6 (2017): e27679. https://doi.org/10.1063/1.4990740 DOI: https://doi.org/10.7554/eLife.27679

Xiao, Fanrong, Jan Hrabe, and Sabina Hrabetova. "Anomalous extracellular diffusion in rat cerebellum." Biophysical Journal 108, no. 9 (2015): 2384-2395. https://doi.org/10.1016/j.bpj.2015.02.034 DOI: https://doi.org/10.1016/j.bpj.2015.02.034

Holter, Karl Erik, Benjamin Kehlet, Anna Devor, Terrence J. Sejnowski, Anders M. Dale, Stig W. Omholt, Ole Petter Ottersen, Erlend Arnulf Nagelhus, Kent-André Mardal, and Klas H. Pettersen. "Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow." Proceedings of the National Academy of Sciences 114, no. 37 (2017): 9894-9899. https://doi.org/10.1073/pnas.1706942114 DOI: https://doi.org/10.1073/pnas.1706942114

Budroni, M. A., and Anne De Wit. "Dissipative structures: From reaction-diffusion to chemo-hydrodynamic patterns." Chaos: An Interdisciplinary Journal of Nonlinear Science 27, no. 10 (2017): 104617. https://doi.org/10.1063/1.4990740 DOI: https://doi.org/10.1063/1.4990740

D’Hernoncourt, Jessica, A. Zebib, and Anne De Wit. "On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts." Chaos: An Interdisciplinary Journal of Nonlinear Science 17, no. 1 (2007): 013109. https://doi.org/10.1063/1.2405129 DOI: https://doi.org/10.1063/1.2405129

D’Hernoncourt, Jessica, A. Zebib, and Anne De Wit. "Reaction driven convection around a stably stratified chemical front." Physical review letters 96, no. 15 (2006): 154501. https://doi.org/10.1103/physrevlett.96.154501 DOI: https://doi.org/10.1103/PhysRevLett.96.154501

Loodts, Vanessa, Carelle Thomas, Laurence Rongy, and Anne De Wit. "Control of convective dissolution by chemical reactions: General classification and application to CO 2 dissolution in reactive aqueous solutions." Physical review letters 113, no. 11 (2014): 114501. https://doi.org/10.1103/physrevlett.113.114501 DOI: https://doi.org/10.1103/PhysRevLett.113.114501

Jotkar, Mamta, Anne De Wit, and Laurence Rongy. "Control of chemically driven convective dissolution by differential diffusion effects." Physical Review Fluids 6, no. 5 (2021): 053504. https://doi.org/10.5194/egusphere-egu21-8718 DOI: https://doi.org/10.1103/PhysRevFluids.6.053504

Budroni, M. A., Carelle Thomas, and Anne De Wit. "Chemical control of dissolution-driven convection in partially miscible systems: nonlinear simulations and experiments." Physical Chemistry Chemical Physics 19, no. 11 (2017): 7936-7946. https://doi.org/10.1039/c6cp08434f DOI: https://doi.org/10.1039/C6CP08434F

Loodts, Vanessa, Laurence Rongy, and Anne De Wit. "Chemical control of dissolution-driven convection in partially miscible systems: theoretical classification." Physical Chemistry Chemical Physics 17, no. 44 (2015): 29814-29823. https://doi.org/10.1039/c5cp03082 DOI: https://doi.org/10.1039/C5CP03082J

Balakotaiah, Vemuri, Sandra MS Dommeti, and Nikunj Gupta. "Bifurcation analysis of chemical reactors and reacting flows." Chaos: An Interdisciplinary Journal of Nonlinear Science 9, no. 1 (1999): 13-35. https://doi.org/10.1063/1.166377 DOI: https://doi.org/10.1063/1.166377

Ghoshal, Parama, and Silvana SS Cardoso. "Reactive convective-dissolution in a porous medium: stability and nonlinear dynamics." Physical Chemistry Chemical Physics 20, no. 33 (2018): 21617-21628. https://doi.org/10.1039/c8cp03064b DOI: https://doi.org/10.1039/C8CP03064B

Goncalves, Eric, Regiane Fortes Patella, Julien Rolland, Benoit Pouffary, and Guillaume Challier. "Thermodynamic effect on a cavitating inducer in liquid hydrogen." Journal of fluids engineering 132, no. 11 (2010). https://doi.org/10.1115/1.4002886 DOI: https://doi.org/10.1115/1.4002886

Lecoanet, Daniel, Josiah Schwab, Eliot Quataert, Lars Bildsten, F. X. Timmes, Keaton J. Burns, Geoffrey M. Vasil, Jeffrey S. Oishi, and Benjamin P. Brown. "Turbulent chemical diffusion in convectively bounded carbon flames." The Astrophysical Journal 832, no. 1 (2016): 71. https://doi.org/10.3847/0004-637x/832/1/71 DOI: https://doi.org/10.3847/0004-637X/832/1/71

Zhou, Quan, and Ke-Qing Xia. "Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection." Physical Review E 77, no. 5 (2008): 056312. https://doi.org/10.1103/physreve.77.056312 DOI: https://doi.org/10.1103/PhysRevE.77.056312

Chalamalla, Vamsi K., and Sutanu Sarkar. "Mixing, dissipation rate, and their overturn-based estimates in a near-bottom turbulent flow driven by internal tides." Journal of Physical Oceanography 45, no. 8 (2015): 1969-1987. https://doi.org/10.1175/jpo-d-14-0057.1 DOI: https://doi.org/10.1175/JPO-D-14-0057.1

Eckert, E. R. G., L. S. Jurewicz, and O. E. Tewfik. "Diffusion-thermo effects on heat transfer from a cylinder in cross flow." AIAA Journal 1, no. 7 (1963): 1537-1543. https://doi.org/10.2514/3.1852 DOI: https://doi.org/10.2514/3.1852

Sumithra, R., Deepa R. Acharya, and M. A. Archana. "Two Component Non-Darcian Benard Marangoni Convection with Uniform and Non-Uniform Temperature Gradients in a Composite Layer with Variable Heat Sources/Sinks." Journal of Mines, Metals and Fuels (2022): 112-131. https://doi.org/10.18311/jmmf/2022/31859 DOI: https://doi.org/10.18311/jmmf/2022/31859

Venables, Emily, Keith Nicholls, Fabian Wolk, Keith Makinson, and Paul Anker. "Measuring turbulent dissipation rates beneath an Antarctic ice shelf." Marine Technology Society Journal 48, no. 5 (2014): 18-24. https://doi.org/10.4031/mtsj.48.5.8 DOI: https://doi.org/10.4031/MTSJ.48.5.8

Silva, Luis, James F. Mather, and Radostin D. Simitev. "The onset of thermo-compositional convection in rotating spherical shells." Geophysical & Astrophysical Fluid Dynamics 113, no. 4 (2019): 377-404. https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.002 DOI: https://doi.org/10.1080/03091929.2019.1640875

Masuda, Yoshio, Michio Yoneya, Akira Suzuki, Shigeo Kimura, and Farid Alavyoon. "Numerical analysis of double-diffusive convection in a porous enclosure due to opposing heat and mass fluxes on the vertical walls–Why does peculiar oscillation occur?." International journal of heat and mass transfer 51, no. 1-2 (2008): 383-388. https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.002 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.002

Ross, Tetjana, and Andone Lavery. "Acoustic detection of oceanic double-diffusive convection: a feasibility study." Journal of Atmospheric and Oceanic Technology 27, no. 3 (2010): 580-593. https://doi.org/10.1175/2009jtecho696.1 DOI: https://doi.org/10.1175/2009JTECHO696.1

Zaussinger, Florian, and Friedrich Kupka. "Layer formation in double-diffusive convection over resting and moving heated plates." Theoretical and Computational Fluid Dynamics 33 (2019): 383-409. https://doi.org/10.1007/s00162-019-00499-7 DOI: https://doi.org/10.1007/s00162-019-00499-7

Sumithra, R., Shyamala Venkatraman, and R. K. Vanishree. "Impact of Magnetic Field on the Onset of Double Diffusive Rayleigh-Benard Convection Governed by Local Thermal Non-Equilibrium in a Double Layered System." Journal of Mines, Metals & Fuels 70 (2022). https://doi.org/10.18311/jmmf/2022/31850 DOI: https://doi.org/10.18311/jmmf/2022/31850

Manjunatha, N., R. Sumithra, and R. K. Vanishree. "Darcy-Benard double diffusive Marangoni convection in a composite layer system with constant heat source along with non-uniform temperature gradients." Malaysian Journal of Fundamental and Applied Sciences 17, no. 1 (2021): 7-15. https://doi.org/10.11113/mjfas.v17n1.1984 DOI: https://doi.org/10.11113/mjfas.v17n1.1984

Wu, Shuonan, and Jinchao Xu. "Simplex-averaged finite element methods for H (grad), H (curl), and H (div) convection-diffusion problems." SIAM Journal on Numerical Analysis 58, no. 1 (2020): 884-906. https://doi.org/10.1137/18m1227196 DOI: https://doi.org/10.1137/18M1227196

Barrenechea, Gabriel R., Volker John, Petr Knobloch, and Richard Rankin. "A unified analysis of algebraic flux correction schemes for convection–diffusion equations." SeMA Journal 75 (2018): 655-685. https://doi.org/10.1007/s40324-018-0160-6 DOI: https://doi.org/10.1007/s40324-018-0160-6

Chertock, Alina, Charles R. Doering, Eugene Kashdan, and Alexander Kurganov. "A fast-explicit operator splitting method for passive scalar advection." Journal of Scientific Computing 45 (2010): 200-214. https://doi.org/10.1007/s10915-010-9381-2 DOI: https://doi.org/10.1007/s10915-010-9381-2

Ullmann, Elisabeth, Howard C. Elman, and Oliver G. Ernst. "Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems." SIAM Journal on Scientific Computing 34, no. 2 (2012): A659-A682. https://doi.org/10.1137/110836675 DOI: https://doi.org/10.1137/110836675

Angermann, Lutz. "A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations." Numerische Mathematik 85 (2000): 175-195. https://doi.org/10.1007/pl00005385 DOI: https://doi.org/10.1007/PL00005385

Patel, Yogeshwari, and Jayesh M. Dhodiya. "Application of differential transform method to solve linear, non-linear reaction convection diffusion and convection diffusion problem." International Journal of Pure and Applied Mathematics 109, no. 3 (2016): 529-538. https://doi.org/10.12732/ijpam.v109i3.4 DOI: https://doi.org/10.12732/ijpam.v109i3.4

Zhi, Xiaoli, Rong Lu, and Xinda Lu. "Universal parallel solver for convection-diffusion equations." Parallel processing letters 14, no. 01 (2004): 107-117. https://doi.org/10.1142/s0129626404001751 DOI: https://doi.org/10.1142/S0129626404001751

Garbey, Marc, Yu A. Kuznetsov, and Yu V. Vassilevski. "A parallel Schwarz method for a convection-diffusion problem." SIAM Journal on Scientific Computing 22, no. 3 (2000): 891-916. https://doi.org/10.1137/s1064827598335854 DOI: https://doi.org/10.1137/S1064827598335854

Kubrak, Boris, H. Herlina, Friedrich Greve, and Jan G. Wissink. "Low-diffusivity scalar transport using a WENO scheme and dual meshing." Journal of Computational Physics 240 (2013): 158-173. https://doi.org/10.1016/j.jcp.2012.12.039 DOI: https://doi.org/10.1016/j.jcp.2012.12.039

Abdullah, Aslam. "A simulation method of 2d steady scalar convection-diffusion flow on an exponentially graded mesh." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 105, no. 1 (2023): 76-89. https://doi.org/10.37934/arfmts.105.1.7689 DOI: https://doi.org/10.37934/arfmts.105.1.7689

Heffernan, Conor, and Colm-cille P. Caulfield. "Robust and efficient identification of optimal mixing perturbations using proxy multiscale measures." Philosophical Transactions of the Royal Society A 380, no. 2225 (2022): 20210026. https://doi.org/10.1098/rsta.2021.0026 DOI: https://doi.org/10.1098/rsta.2021.0026

Alqahtani, Mnerh, Leonardo Grigorio, and Tobias Grafke. "Extreme events and instantons in Lagrangian passive scalar turbulence models." Physical Review E 106, no. 1 (2022): 015101. https://doi.org/10.48550/arxiv.2108.02103 DOI: https://doi.org/10.1103/PhysRevE.106.015101

Sreenivasan, Katepalli R. "Turbulent mixing: A perspective." Proceedings of the National Academy of Sciences 116, no. 37 (2019): 18175-18183. https://doi.org/10.1073/pnas.1800463115 DOI: https://doi.org/10.1073/pnas.1800463115

Karasso, P. S., and M. G. Mungal. "Mixing and reaction in curved liquid shear layers." Journal of Fluid Mechanics 334 (1997): 381-409. https://doi.org/10.1017/s0022112096004430 DOI: https://doi.org/10.1017/S0022112096004430

Karasso, P. S., and M. G. Mungal. "Scalar mixing and reaction in plane liquid shear layers." Journal of Fluid Mechanics 323 (1996): 23-63. https://doi.org/10.1017/s0022112096000833 DOI: https://doi.org/10.1017/S0022112096000833

Cai, J., M. J. Dinger, W. Li, C. D. Carter, M. D. Ryan, and C. Tong. "Experimental study of three-scalar mixing in a turbulent coaxial jet." Journal of fluid mechanics 685 (2011): 495-531. https://doi.org/10.1017/jfm.2011.337 DOI: https://doi.org/10.1017/jfm.2011.337

Fox, Rodney O. "On velocity‐conditioned scalar mixing in homogeneous turbulence." Physics of Fluids 8, no. 10 (1996): 2678-2691. https://doi.org/10.1063/1.869054 DOI: https://doi.org/10.1063/1.869054

de Bruyn Kops, Stephen M., and Mikael Mortensen. "Conditional mixing statistics in a self-similar scalar mixing layer." Physics of Fluids 17, no. 9 (2005): 095107. https://doi.org/10.1063/1.2055467 DOI: https://doi.org/10.1063/1.2055467

Published

2024-11-30

How to Cite

Abdullah, A. ., Mohd Yunos, S. N. M. ., & Basuno, B. . (2024). A Comprehensive Review of Recent Advances in Scalar Convection- Diffusion Studies. Journal of Advanced Research in Numerical Heat Transfer, 27(1), 14–27. https://doi.org/10.37934/arnht.27.1.1427

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