PROST swMATH ID: 12822 Software Authors: Renardy, Yuriko; Renardy, Michael Description: PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. Volume-of-fluid (VOF) methods are popular for the direct numerical simulation of time-dependent viscous incompressible flow of multiple liquids. As in any numerical method, however, it has its weaknesses, namely, for flows in which the capillary force is the dominant physical mechanism. The lack of convergence with spatial refinement, or convergence to a solution that is slightly different from the exact solution, has been documented in the literature. A well-known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity. These currents are present in all previous versions of VOF algorithms. In this paper, we develop an accurate representation of the body force due to surface tension, which effectively eliminates spurious currents. We call this algorithm PROST: parabolic reconstruction of surface tension. There are several components to this procedure, including the new body force algorithm, improvements in the projection method for the Navier-Stokes solver, and a higher order interface advection scheme. The curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999102971901 Keywords: volume-of-fluid method; continuous surface force; multiphase flow Related Software: Gerris; SLIC; KRAKEN; VOFTools; OpenFOAM; NASA-VOF2D; InterFOAM; RIPPLE; voFoam; Gmsh; PETSc; FLUENT; p4est; FELSOS; ALBERTA; FEATFLOW; hypre; SOLA-VOF; Keras; TensorFlow Referenced in: 168 Publications all top 5 Referenced by 356 Authors 8 Renardy, Yuriko Yamamuro 7 Afkhami, Shahriar 6 López, Joaquín 5 Francois, Marianne M. 5 Hernández, Juan José 5 Popinet, Stéphane 5 Sussman, Mark 5 Tomar, Gaurav 4 Caboussat, Alexandre 4 Gibou, Frédéric 4 Gomez, Pablo 4 Kim, Junseok 4 Zaleski, Stéphane 3 Ashgriz, Nasser 3 Biswas, Gautam 3 Cardinaels, Ruth 3 Cristini, Vittorio 3 Denner, Fabian 3 Faura, Félix 3 Fuchs, László 3 Fuster, Daniel 3 Kothe, Douglas B. 3 Lowengrub, John Samuel 3 Moldenaers, Paula 3 Mostaghimi, Javad 3 Nürnberg, Robert 3 Shirani, Ebrahim 3 van Wachem, Berend G. M. 3 Xiao, Feng 3 Zanzi, Claudio 2 Barrett, John William 2 Bruchon, Julien 2 Buscaglia, Gustavo Carlos 2 Bussmann, Markus 2 Cifani, Paolo 2 Drapier, Sylvain 2 Evrard, Fabien 2 Garcke, Harald 2 Geurts, Bernard J. 2 Herrmann, Marcus 2 Ito, Kei 2 James, Ashley J. 2 Jofre, Lluís 2 Juric, Damir 2 Kuerten, J. G. M. 2 Kunugi, Tomoaki 2 Larios-Cárdenas, Luis Ángel 2 Le Chenadec, Vincent 2 Lee, Hyun Geun 2 Legendre, Dominique 2 Lörstad, Daniel 2 Luo, Lishi 2 Manservisi, Sandro 2 Marić, Tomislav 2 Muñoz, Daniel Pino 2 Ni, Mingjiu 2 Nourgaliev, Robert R. 2 Ohshima, Hiroyuki 2 Ohta, Mitsuhiro 2 Oliva, Assensi 2 Owkes, Mark 2 Picasso, Marco 2 Pitsch, Heinz 2 Raessi, Mehdi 2 Saito, Kozo 2 Salazar, Abraham J. 2 Scardovelli, Ruben 2 Sharma, Ashutosh 2 Shin, Seungwon 2 Sicilian, James M. 2 Srinivasan, Vedanth 2 Tong, Albert Y. 2 Valdivieso, François 2 Verhulst, Kristof 2 Vincent, Stéphane 2 Wang, Zhaoyuan 2 Xie, Bin 2 Yang, Aiming 2 Yang, Xiaofeng 2 Yokoi, Kensuke 2 Zheng, Xiaoming 1 Abadie, T. 1 Abdel-Khalik, S. I. 1 Abgrall, Rémi 1 Aboukhedr, M. 1 Abu-Al-Saud, Moataz O. 1 Agbaglah, Gilou 1 Agnese, Marco 1 Ahmad, Suhail 1 Akkerman, Ido 1 Alam, Sharf 1 An, Ruidong 1 Anderson, Anthony M. 1 Anderson, Patrick D. 1 Aniszewski, Wojciech 1 Antepara, Oscar 1 Anumolu, Lakshman 1 Auguste, Franck 1 Aulisa, Eugenio 1 Ausas, Roberto Federico ...and 256 more Authors all top 5 Referenced in 26 Serials 72 Journal of Computational Physics 22 Computers and Fluids 12 International Journal for Numerical Methods in Fluids 8 Physics of Fluids 7 Applied Mathematical Modelling 6 Computer Methods in Applied Mechanics and Engineering 4 Journal of Non-Newtonian Fluid Mechanics 3 International Journal for Numerical Methods in Engineering 3 SIAM Journal on Scientific Computing 3 European Journal of Mechanics. B. Fluids 2 Computers & Mathematics with Applications 2 Journal of Fluid Mechanics 2 SIAM Journal on Numerical Analysis 2 Journal of Scientific Computing 2 International Journal of Computational Fluid Dynamics 2 Archives of Computational Methods in Engineering 1 General Relativity and Gravitation 1 International Journal of Heat and Mass Transfer 1 Physica A 1 Fluid Dynamics Research 1 Applied Mathematics and Mechanics. (English Edition) 1 Mathematical and Computer Modelling 1 International Journal of Computational Methods 1 International Journal of Numerical Analysis and Modeling 1 Communications in Applied Mathematics and Computational Science 1 Communications in Computational Physics all top 5 Referenced in 9 Fields 158 Fluid mechanics (76-XX) 52 Numerical analysis (65-XX) 8 Mechanics of deformable solids (74-XX) 6 Partial differential equations (35-XX) 3 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Referencing Publications by Year