A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows

Corcos, Luke P.; Saye, Robert I.; Sethian, James A.

doi:10.1016/j.jcp.2024.112960

Title: A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows

Journal Article · 31 May 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.112960 · OSTI ID:2329347

Corcos, Luke P.;

; Sethian, James A.

Not Available

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

OSTI ID:: 2329347

Alternate ID(s):: OSTI ID: 2397250

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 507; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (70)

Fundamental Fluid Dynamics Challenges in Inkjet Printing Lohse, Detlef Annual Review of Fluid Mechanics, Vol. 54, Issue 1 https://doi.org/10.1146/annurev-fluid-022321-114001	journal	January 2022
E XPERIMENTS ON T HERMOCAPILLARY I NSTABILITIES Schatz, Michael F.; Neitzel, G. Paul Annual Review of Fluid Mechanics, Vol. 33, Issue 1 https://doi.org/10.1146/annurev.fluid.33.1.93	journal	January 2001
A level-set method for two-phase flows with soluble surfactant Xu, Jian-Jun; Shi, Weidong; Lai, Ming-Chih Journal of Computational Physics, Vol. 353 https://doi.org/10.1016/j.jcp.2017.10.019	journal	January 2018
A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation Son, Gihun International Communications in Heat and Mass Transfer, Vol. 58 https://doi.org/10.1016/j.icheatmasstransfer.2014.08.024	journal	November 2014
Dynamics and stability of thin liquid films Craster, R. V.; Matar, O. K. Reviews of Modern Physics, Vol. 81, Issue 3 https://doi.org/10.1103/RevModPhys.81.1131	journal	August 2009
Evaporation of Water Droplets Placed on a Heated Horizontal Surface Ruiz, Orlando E.; Black, William Z. Journal of Heat Transfer, Vol. 124, Issue 5 https://doi.org/10.1115/1.1494092	journal	September 2002
The Critical Role of Solvent Evaporation on the Roughness of Spin-Cast Polymer Films Strawhecker, Kenneth E.; Kumar, Sanat K.; Douglas, Jack F. Macromolecules, Vol. 34, Issue 14 https://doi.org/10.1021/ma001440d	journal	July 2001
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems Cockburn, Bernardo; Shu, Chi-Wang SIAM Journal on Numerical Analysis, Vol. 35, Issue 6 https://doi.org/10.1137/S0036142997316712	journal	December 1998
The Marangoni Effects Scriven, L. E.; Sternling, C. V. Nature, Vol. 187, Issue 4733 https://doi.org/10.1038/187186a0	journal	July 1960
Analysis of the Effects of Marangoni Stresses on the Microflow in an Evaporating Sessile Droplet Hu, Hua; Larson, Ronald G. Langmuir, Vol. 21, Issue 9 https://doi.org/10.1021/la0475270	journal	April 2005
Fast multigrid solution of high-order accurate multiphase Stokes problems Saye, Robert Communications in Applied Mathematics and Computational Science, Vol. 15, Issue 2 https://doi.org/10.2140/camcos.2020.15.33	journal	January 2020
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II Saye, Robert Journal of Computational Physics, Vol. 344 https://doi.org/10.1016/j.jcp.2017.05.003	journal	September 2017
The levelling of paints Overdiep, W. S. Progress in Organic Coatings, Vol. 14, Issue 2 https://doi.org/10.1016/0033-0655(86)80010-3	journal	October 1986
A Level Set Method for vaporizing two-phase flows Tanguy, Sébastien; Ménard, Thibaut; Berlemont, Alain Journal of Computational Physics, Vol. 221, Issue 2 https://doi.org/10.1016/j.jcp.2006.07.003	journal	February 2007
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo SIAM Journal on Numerical Analysis, Vol. 39, Issue 5 https://doi.org/10.1137/S0036142901384162	journal	January 2002
Interfacial Phenomena in Liquid Extraction Sherwood, Thomas; Wei, James Industrial & Engineering Chemistry, Vol. 49, Issue 6 https://doi.org/10.1021/ie50570a038	journal	June 1957
Interface-resolved detailed numerical simulation of evaporating two-phase flows with robin boundary conditions on irregular domains Chai, Min; Luo, Kun; Shao, Changxiao International Journal of Heat and Mass Transfer, Vol. 145 https://doi.org/10.1016/j.ijheatmasstransfer.2019.118774	journal	December 2019
Long-scale evolution of thin liquid films Oron, Alexander; Davis, Stephen H.; Bankoff, S. George Reviews of Modern Physics, Vol. 69, Issue 3 https://doi.org/10.1103/RevModPhys.69.931	journal	July 1997
Interfacial gauge methods for incompressible fluid dynamics Saye, Robert Science Advances, Vol. 2, Issue 6 https://doi.org/10.1126/sciadv.1501869	journal	June 2016
Insights from high-fidelity modeling of industrial rotary bell atomization Saye, Robert I.; Sethian, James A.; Petrouskie, Brandon Proceedings of the National Academy of Sciences, Vol. 120, Issue 4 https://doi.org/10.1073/pnas.2216709120	journal	January 2023
A mathematical model for drying paint layers Howison, S. D.; Moriarty, J. A.; Ockendon, J. R. Journal of Engineering Mathematics, Vol. 32, Issue 4, p. 377-394 https://doi.org/10.1023/A:1004224014291	journal	January 1997
High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles Saye, R. I. SIAM Journal on Scientific Computing, Vol. 37, Issue 2 https://doi.org/10.1137/140966290	journal	January 2015
Hydrodynamic model of steady movement of a solid/liquid/fluid contact line Huh, Chun; Scriven, L. E. Journal of Colloid and Interface Science, Vol. 35, Issue 1 https://doi.org/10.1016/0021-9797(71)90188-3	journal	January 1971
Marangoni convection induced by simultaneous mass and heat transfer during evaporation of n-heptane/ether binary liquid mixture Zhong, Yixing; Zhuo, Yayun; Wang, Zhenfeng International Journal of Heat and Mass Transfer, Vol. 108 https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.038	journal	May 2017
Recent Developments in Rayleigh-Bénard Convection Bodenschatz, Eberhard; Pesch, Werner; Ahlers, Guenter Annual Review of Fluid Mechanics, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.fluid.32.1.709	journal	January 2000
A Case Study in Striation Prevention by Targeted Formulation Adjustment: Aluminum Titanate Sol−Gel Coatings Taylor, D. J.; Birnie, Dunbar P. Chemistry of Materials, Vol. 14, Issue 4 https://doi.org/10.1021/cm010192c	journal	March 2002
Nitsche’s method for general boundary conditions Juntunen, Mika; Stenberg, Rolf Mathematics of Computation, Vol. 78, Issue 267 https://doi.org/10.1090/S0025-5718-08-02183-2	journal	September 2009
On convection cells induced by surface tension Pearson, J. R. A. Journal of Fluid Mechanics, Vol. 4, Issue 5 https://doi.org/10.1017/S0022112058000616	journal	September 1958
Transport and diffusion of material quantities on propagating interfaces via level set methods Adalsteinsson, David; Sethian, J. A. Journal of Computational Physics, Vol. 185, Issue 1 https://doi.org/10.1016/S0021-9991(02)00057-8	journal	February 2003
An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions Donea, J.; Giuliani, S.; Halleux, J. P. Computer Methods in Applied Mechanics and Engineering, Vol. 33, Issue 1-3 https://doi.org/10.1016/0045-7825(82)90128-1	journal	September 1982
Efficient multigrid solution of elliptic interface problems using viscosity-upwinded local discontinuous Galerkin methods Saye, Robert I. Communications in Applied Mathematics and Computational Science, Vol. 14, Issue 2 https://doi.org/10.2140/camcos.2019.14.247	journal	January 2019
Surface deformation and film corrugation during drying of polymer solutions induced by Marangoni phenomena Yiantsios, Stergios G.; Serpetsi, Stefania K.; Doumenc, Frédéric International Journal of Heat and Mass Transfer, Vol. 89 https://doi.org/10.1016/j.ijheatmasstransfer.2015.06.015	journal	October 2015
Marangoni Convection With a Curved and Deforming Free Surface in a Cavity Sasmal, G. P.; Hochstein, J. I. Journal of Fluids Engineering, Vol. 116, Issue 3 https://doi.org/10.1115/1.2910316	journal	September 1994
Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study Bhardwaj, Rajneesh; Fang, Xiaohua; Attinger, Daniel New Journal of Physics, Vol. 11, Issue 7 https://doi.org/10.1088/1367-2630/11/7/075020	journal	July 2009
Thermocapillary Instabilities Davis, S. H. Annual Review of Fluid Mechanics, Vol. 19, Issue 1 https://doi.org/10.1146/annurev.fl.19.010187.002155	journal	January 1987
On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity Scriven, L. E.; Sternling, C. V. Journal of Fluid Mechanics, Vol. 19, Issue 3 https://doi.org/10.1017/S0022112064000751	journal	July 1964
Les tourbillons cellulaires dans une nappe liquide. - Méthodes optiques d'observation et d'enregistrement Bénard, Henri Journal de Physique Théorique et Appliquée, Vol. 10, Issue 1 https://doi.org/10.1051/jphystap:0190100100025400	journal	January 1901
Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces Bochkov, Daniil; Gibou, Frederic Journal of Computational Physics, Vol. 376 https://doi.org/10.1016/j.jcp.2018.10.020	journal	January 2019
Evaporation and Marangoni Driven Convection in Small Heated Water Droplets Girard, Fabien; Antoni, Mickaël; Faure, Sylvain Langmuir, Vol. 22, Issue 26 https://doi.org/10.1021/la061572l	journal	November 2006
Surface Tension as the Cause of Bénard Cells and Surface Deformation in a Liquid Film Block, Myron J. Nature, Vol. 178, Issue 4534 https://doi.org/10.1038/178650a0	journal	September 1956
Pattern formation and mass transfer under stationary solutal Marangoni instability Schwarzenberger, Karin; Köllner, Thomas; Linde, Hartmut Advances in Colloid and Interface Science, Vol. 206 https://doi.org/10.1016/j.cis.2013.10.003	journal	April 2014
The Effect of Monomolecular Films on the Evaporation of Ether Solutions. Langmuir, Irving; Langmuir, D. B. The Journal of Physical Chemistry, Vol. 31, Issue 11 https://doi.org/10.1021/j150281a011	journal	November 1927
Three-Dimensional Direct Numerical Simulation of Surface-Tension-Gradient Effects on the Leveling of an Evaporating Multicomponent Fluid Eres, M. H.; Weidner, D. E.; Schwartz, L. W. Langmuir, Vol. 15, Issue 5 https://doi.org/10.1021/la980414u	journal	February 1999
Marangoni effects of trace impurities on the motion of long gas bubbles in capillaries Ratulowski, J.; Chang, H. -C. Journal of Fluid Mechanics, Vol. 210 https://doi.org/10.1017/S0022112090001306	journal	January 1990
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I Saye, Robert Journal of Computational Physics, Vol. 344 https://doi.org/10.1016/j.jcp.2017.04.076	journal	September 2017
Multiscale structures in solutal Marangoni convection: Three-dimensional simulations and supporting experiments Köllner, Thomas; Schwarzenberger, Karin; Eckert, Kerstin Physics of Fluids, Vol. 25, Issue 9 https://doi.org/10.1063/1.4821536	journal	September 2013
The leveling of thermosetting waterborne coatings. Part I: Observation of leveling process Kojima, Shunji; Moriga, Toshinori; Takenouchi, Ken Polymer Engineering & Science, Vol. 33, Issue 20 https://doi.org/10.1002/pen.760332004	journal	October 1993
Level-set simulations of soluble surfactant driven flows Cleret de Langavant, Charles; Guittet, Arthur; Theillard, Maxime Journal of Computational Physics, Vol. 348 https://doi.org/10.1016/j.jcp.2017.07.003	journal	November 2017
The moving contact line: the slip boundary condition Dussan V., E. B. Journal of Fluid Mechanics, Vol. 77, Issue 4 https://doi.org/10.1017/S0022112076002838	journal	October 1976
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) Fedkiw, Ronald P.; Aslam, Tariq; Merriman, Barry Journal of Computational Physics, Vol. 152, Issue 2 https://doi.org/10.1006/jcph.1999.6236	journal	July 1999
XLII. On certain curious motions observable at the surfaces of wine and other alcoholic liquors Thomson, James The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 10, Issue 67 https://doi.org/10.1080/14786445508641982	journal	November 1855
Long-wavelength surface-tension-driven Bénard convection: experiment and theory Vanhook, Stephen J.; Schatz, Michael F.; Swift, J. B. Journal of Fluid Mechanics, Vol. 345 https://doi.org/10.1017/S0022112097006101	journal	August 1997
Study on different planforms of paint’s solvents and the effect of surfactants (on them) Abbasian, A.; Ghaffarian, S. R.; Mohammadi, N. Progress in Organic Coatings, Vol. 49, Issue 3 https://doi.org/10.1016/j.porgcoat.2003.09.020	journal	April 2004
Surface-only ferrofluids Huang, Libo; Michels, Dominik L. ACM Transactions on Graphics, Vol. 39, Issue 6 https://doi.org/10.1145/3414685.3417799	journal	November 2020
Numerical simulation of two-phase flows with heat and mass transfer Bänsch, Eberhard; Basting, Steffen Discrete & Continuous Dynamical Systems - A, Vol. 35, Issue 6 https://doi.org/10.3934/dcds.2015.35.2325	journal	January 2015
Ueber die Ausbreitung der Tropfen einer Flüssigkeit auf der Oberfläche einer anderen Marangoni, Carl Annalen der Physik und Chemie, Vol. 219, Issue 7 https://doi.org/10.1002/andp.18712190702	journal	January 1871
L EVEL S ET M ETHODS FOR F LUID I NTERFACES Sethian, J. A.; Smereka, Peter Annual Review of Fluid Mechanics, Vol. 35, Issue 1 https://doi.org/10.1146/annurev.fluid.35.101101.161105	journal	January 2003
Efficient Operator-Coarsening Multigrid Schemes for Local Discontinuous Galerkin Methods Fortunato, Daniel; Rycroft, Chris H.; Saye, Robert SIAM Journal on Scientific Computing, Vol. 41, Issue 6 https://doi.org/10.1137/18M1206357	journal	January 2019
A finite difference discretization method for heat and mass transfer with Robin boundary conditions on irregular domains Chai, Min; Luo, Kun; Shao, Changxiao Journal of Computational Physics, Vol. 400 https://doi.org/10.1016/j.jcp.2019.108890	journal	January 2020
Role of Bénard−Marangoni Instabilities during Solvent Evaporation in Polymer Surface Corrugations Bassou, N.; Rharbi, Y. Langmuir, Vol. 25, Issue 1 https://doi.org/10.1021/la802979a	journal	November 2008
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations Osher, Stanley; Sethian, James A. Journal of Computational Physics, Vol. 79, Issue 1 https://doi.org/10.1016/0021-9991(88)90002-2	journal	November 1988
Some evidence for the existence and magnitude of a critical marangoni number for the onset of oscillatory flow in crystal growth melts Schwabe, D.; Scharmann, A. Journal of Crystal Growth, Vol. 46, Issue 1 https://doi.org/10.1016/0022-0248(79)90119-2	journal	January 1979
Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions Papac, Joseph; Gibou, Frédéric; Ratsch, Christian Journal of Computational Physics, Vol. 229, Issue 3 https://doi.org/10.1016/j.jcp.2009.10.017	journal	February 2010
Level set method for atomization and evaporation simulations Luo, Kun; Shao, Changxiao; Chai, Min Progress in Energy and Combustion Science, Vol. 73 https://doi.org/10.1016/j.pecs.2019.03.001	journal	July 2019
Interfacial turbulence: Hydrodynamic instability and the marangoni effect Sternling, C. V.; Scriven, L. E. AIChE Journal, Vol. 5, Issue 4 https://doi.org/10.1002/aic.690050421	journal	December 1959
Instabilities during the evaporation of a film: Non-glassy polymer + volatile solvent de Gennes, P. G. The European Physical Journal E, Vol. 6, Issue 5, p. 421-424 https://doi.org/10.1007/s10189-001-8055-3	journal	December 2001
The Voronoi Implicit Interface Method for computing multiphase physics Saye, R. I.; Sethian, J. A. Proceedings of the National Academy of Sciences, Vol. 108, Issue 49 https://doi.org/10.1073/pnas.1111557108	journal	November 2011
Drying of thin colloidal films Routh, Alexander F. Reports on Progress in Physics, Vol. 76, Issue 4 https://doi.org/10.1088/0034-4885/76/4/046603	journal	March 2013
A level-set continuum method for two-phase flows with insoluble surfactant Xu, Jian-Jun; Yang, Yin; Lowengrub, John Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.05.014	journal	July 2012
A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect Rueda Villegas, Lucia; Alis, Romain; Lepilliez, Mathieu Journal of Computational Physics, Vol. 316 https://doi.org/10.1016/j.jcp.2016.04.031	journal	July 2016

Similar Records

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

Journal Article · 2014 · Computers and Fluids · OSTI ID:1177217

Xia, Yidong; Luo, Hong; Frisbey, Megan; +1 more

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

Journal Article · 2017 · Journal of Computational Physics · OSTI ID:1379921

Saye, Robert

Journal Article · 2017 · Journal of Computational Physics · OSTI ID:1379922

Saye, Robert

Title: A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows

Citation Formats

References (70)

Similar Records

Related Subjects