Barrett JW, Garcke H, Nürnberg R. Numerical computations of the dynamics of fluidic membranes and vesicles. Phys Rev E. 2015;92:052704.
Edwards DA, Brenner H, Wasan DT. Interfacial Transport Processes and Rheology. Boston, MA: Butterworth-Heinemann; 1991.
Grassia P, Ubal S, Giavedoni MD, Vitasari D, Martin PJ. Surfactant flow between a plateau border and a film during foam fractionation. Chem Eng Sci. 2016;143:139-165.
O'Brien S, Schwartz L. Theory and modeling of thin film flows. Encyclopedia of Surface and Colloid Science. 2002;1:5283-5297. https://www.semanticscholar.org/paper/THEORY-AND-MODELING-OF-THIN-FILM-FLOWS-O’Brien-Schwartz/1cc51908e0dd5fbf43a8b8ed481844a1fc28f8e3.
Stam J. Flows on surfaces of arbitrary topology. ACM Transactions on Graphics. San Diego, California. 2003;22(3):724-731. http://dx.doi.org/10.1145/882262.882338.
Chan CH, Czubak M, Disconzi MM. The formulation of the Navier–Stokes equations on Riemannian manifolds. J Geom Phys. 2017;121:335-346.
Jankuhn T, Olshanskii M, Reusken A. Incompressible fluid problems on embedded surfaces: Modeling and variational formulations. Interfaces and Free Boundaries. 2018;20(3):353-377. http://dx.doi.org/10.4171/ifb/405.
Koba H, Liu C, Giga Y. Energetic variational approaches for incompressible fluid systems on an evolving surface. Quart Appl Math. 2017;75(2):359-389.
Miura T-H. On singular limit equations for incompressible fluids in moving thin domains. Q Appl Math. 2018;76(2):215-251.
Boussinesq M. Sur l'existence d'une viscosité superficielle, dans la mince couche de transition séparant un liquide d'un autre fluide contigu. Ann Chim Phys. 1913;29:349-357.
Scriven L. Dynamics of a fluid interface equation of motion for newtonian surface fluids. Chem Eng Sci. 1960;12(2):98-108.
Ebin DG, Marsden J. Groups of diffeomorphisms and the motion of an incompressible fluid. Ann Math. 1970;92(1):102-163.
Auer S, Macdonald C, Treib M, Schneider J, Westermann R. Real-time fluid effects on surfaces using the closest point method. Comput Graph Forum. 2012;31(6):1909-1923.
Auer S, Westermann R. A semi-Lagrangian closest point method for deforming surfaces. Comput Graph Forum. 2013;32(7):207-214.
Gross B, Atzberger P. Hydrodynamic flows on curved surfaces: spectral numerical methods for radial manifold shapes. J Comput Phys. 2018;371:663-689.
Gross B, Trask N, Kuberry P, Atzberger P. Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approach. J Comput Phys. 2020;409:109340.
Fengler MJ, Freeden W. A nonlinear Galerkin scheme involving vector and tensor spherical harmonics for solving the incompressible Navier–Stokes equation on the sphere. SIAM J Sci Comput. 2005;27(3):967-994.
Dritschel DG, Qi W, Marston JB. On the late-time behaviour of a bounded, inviscid two-dimensional flow. J Fluid Mech. 2015;783:1-22.
Qi W, Marston JB. Hyperviscosity and statistical equilibria of Euler turbulence on the torus and the sphere. J Stat Mech Theory Exper. 2014;2014(7):P07020.
Fries T-P. Higher-order surface FEM for incompressible Navier–Stokes flows on manifolds. Int J Numer Methods Fluids. 2018;88(2):55-78.
Olshanskii MA, Yushutin V. A penalty finite element method for a fluid system posed on embedded surface. J Math Fluid Mech. 2019;21(1):14.
Reuther S, Voigt A. Solving the incompressible surface Navier–Stokes equation by surface finite elements. Phys Fluids. 2018;30(1):012107.
März T, Macdonald CB. Calculus on surfaces with general closest point functions. SIAM J Numer Anal. 2012;50(6):3303-3328.
Ruuth SJ, Merriman B. A simple embedding method for solving partial differential equations on surfaces. J Comput Phys. 2008;227(3):1943-1961.
Nitschke I, Voigt A, Wensch J. A finite element approach to incompressible two-phase flow on manifolds. J Fluid Mech. 2012;708:418-438.
Suchde P, Kuhnert J. A fully Lagrangian meshfree framework for PDEs on evolving surfaces. J Comput Phys. 2019;395:38-59.
Domínguez JM, Crespo AJC, Gómez-Gesteira M, Marongiu JC. Neighbour lists in smoothed particle hydrodynamics. Int J Numer Methods Fluids. 2011;67(12):2026-2042.
Drumm C, Tiwari S, Kuhnert J, Bart H-J. Finite pointset method for simulation of the liquid - liquid flow field in an extractor. Comput Chem Eng. 2008;32(12):2946-2957.
Onderik J, Ďurikovič R. Efficient neighbor search for particle-based fluids. J Appl Math Stat Inform. 2008;4(1):29-43.
Jefferies A, Kuhnert J, Aschenbrenner L, Giffhorn U. Finite pointset method for the simulation of a vehicle travelling through a body of water. In: Griebel M, Schweitzer AM, eds. Meshfree Methods for Partial Differential Equations VII. Cham, Switzerland: Springer International Publishing; 2015:205-221.
Suchde P, Kuhnert J, Schröder S, Klar A. A flux conserving meshfree method for conservation laws. Int J Numer Methods Eng. 2017;112(3):238-256.
Suchde P, Kuhnert J. A meshfree generalized finite difference method for surface PDEs. Comput Math Appl. 2019;78(8):2789-2805.
Suchde P, Kuhnert J. Point cloud movement for fully Lagrangian meshfree methods. J Comput Appl Math. 2018;340:89-100.
Pahar G, Dhar A. A robust volume conservative divergence-free ISPH framework for free-surface flow problems. Adv Water Resour. 2016;96:423-437.
Evans MW, Harlow FH, Bromberg E. The Particle-in-Cell Method for Hydrodynamic Calculations. Technical Report. Los Alamos, NM: Los Alamos National Lab; 1957.
Marrone S, Colagrossi A, Touzé DL, Graziani G. Fast free-surface detection and level-set function definition in SPH solvers. J Comput Phys. 2010;229(10):3652-3663.
Saucedo-Zendejo FR, Reséndiz-Flores EO, Kuhnert J. Three-dimensional flow prediction in mould filling processes using a GFDM. Comput Part Mech. 2019;6(3):411-425.
Tiwari S, Kuhnert J. Particle method for simulation of free surface flows. In: Hou TY, Tadmor E, eds. Hyperbolic Problems: Theory, Numerics, Applications: Proceedings of the 9th International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25–29, 2002. Berlin, Heidelberg/Germany: Springer; 2003:889-898.
Kuhnert J, Michel I, Mack R. Fluid structure interaction (FSI) in the meshfree Finite Pointset Method (FPM): theory and applications. In: Griebel M, Schweitzer AM, eds. Meshfree Methods for Partial Differential Equations IX, IWMMPDE2017. Berlin, Heidelberg/Germany: Springer; 2019:73-92.
Bertalmio M, Cheng L-T, Osher S, Sapiro G. Variational problems and partial differential equations on implicit surfaces. J Comput Phys. 2001;174(2):759-780.
Delfour M, Zolesio J. A boundary differential equation for thin shells. J Differ Equ. 1995;119(2):426-449.
Dziuk G. Finite elements for the beltrami operator on arbitrary surfaces. In: Hildebrandt S, Leis R, eds. Partial Differential Equations and Calculus of Variations. Berlin, Heidelberg: Springer Berlin Heidelberg; 1988:142-155.
Williamson DL, Drake JB, Hack JJ, Jakob R, Swarztrauber PN. A standard test set for numerical approximations to the shallow water equations in spherical geometry. J Comput Phys. 1992;102(1):211-224.
Fan C-M, Chu C-N, Šarler B, Li T-H. Numerical solutions of waves-current interactions by generalized finite difference method. Eng Anal Bound Elem. 2019;100:150-163. http://dx.doi.org/10.1016/j.enganabound.2018.01.010.
Gavete L, Ureña F, Benito J, García A, Ureña M, Salete E. Solving second order non-linear elliptic partial differential equations using generalized finite difference method. J Comput Appl Math. 2017;318:378-387. Computational and Mathematical Methods in Science and Engineering CMMSE-2015.
Katz A, Jameson A. Meshless scheme based on alignment constraints. AIAA J. 2010;48(11):2501-2511.
Luo M, Koh CG, Bai W, Gao M. A particle method for two-phase flows with compressible air pocket. Int J Numer Methods Eng. 2016;108:695-721.
Demanet L. Painless, Highly Accurate Discretizations of the Laplacian on a Smooth Manifold. Technical Report. Stanford, CA: Stanford University; 2006.
Liang J, Zhao H. Solving partial differential equations on point clouds. SIAM J Sci Comput. 2013;35(3):A1461-A1486.
Chorin AJ. Numerical solution of the Navier–Stokes equations. Math Comput. 1968;22(104):745-762.
Landau L, Lifschitz E. Lehrbuch der theoretischen Physik, Band VI: Hydrodynamik. 5th ed. Berlin, Germany: Akademie-Verlag; 1991.
van der Vorst HA. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput. 1992;13(2):631-644.
Krishnamurthy V, Levoy M. Fitting smooth surfaces to dense polygon meshes. Paper presented at: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH '96, New Orleans, Louisiana; 1996.
Suchde P, Kuhnert J, Tiwari S. On meshfree GFDM solvers for the incompressible Navier–Stokes equations. Comput Fluids. 2018;165:1-12.