GENSMAC3D: a numerical method for solving unsteady three-dimensional free surface flows. A numerical method for solving three-dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENSMAC, the full Navier–Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user-friendly input data file is employed to allow almost any arbitrary three-dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented.

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  1. Liu, Li; Shen, Yiqing; Liu, Shengping; Yu, Ming: The dual information preserving method for stiff reacting flows (2017)
  2. Cruchaga, Marcela; Battaglia, Laura; Storti, Mario; D’Elía, Jorge: Numerical modeling and experimental validation of free surface flow problems (2016)
  3. Elgeti, S.; Sauerland, H.: Deforming fluid domains within the finite element method: five mesh-based tracking methods in comparison (2016)
  4. Tomé, M. F.; Bertoco, J.; Oishi, C. M.; Araujo, M. S. B.; Cruz, D.; Pinho, F. T.; Vynnycky, M.: A finite difference technique for solving a time strain separable K-BKZ constitutive equation for two-dimensional moving free surface flows (2016)
  5. Tomé, M. F.; Castelo, A.; Nóbrega, J. M.; Carneiro, O. S.; Paulo, G. S.; Pereira, F. T.: Numerical and experimental investigations of three-dimensional container filling with Newtonian viscous fluids (2014)
  6. Mompean, G.; Thais, L.; Tomé, M. F.; Castelo, A.: Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models (2011)
  7. Cruchaga, Marcela; Celentano, Diego; Breitkopf, Piotr; Villon, Pierre; Rassineux, Alain: A surface remeshing technique for a Lagrangian description of 3D two-fluid flow problems (2010)
  8. Tomé, M. F.; McKee, S.; Walters, K.: A computational study of some rheological influences on the “splashing experiment” (2010)
  9. Tomé, M. F.; Paulo, G. S.; Pinho, F. T.; Alves, M. A.: Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows (2010)
  10. Ferreira, V. G.; Kurokawa, F. A.; Oishi, C. M.; Kaibara, M. K.; Castelo, A.; Cuminato, J. A.: Evaluation of a bounded high-order upwind scheme for 3D incompressible free surface flow computations (2009)
  11. Tome, Murilo F.; Silva, Renato A. P.; Oishi, Cassio M.; Mckee, Sean: Numerical solution of the upper-convected Maxwell model for three-dimensional free surface flows (2009)
  12. Mckee, S.; Tomé, M. F.; Ferreira, V. G.; Cuminato, J. A.; Castelo, A.; Sousa, F. S.; Mangiavacchi, N.: The MAC method (2008)
  13. Oishi, Cassio M.; Tomé, Murilo F.; Cuminato, José A.; McKee, Sean: An implicit technique for solving 3D low Reynolds number moving free surface flows (2008)
  14. Oishi, C. M.; Cuminato, J. A.; Yuan, J. Y.; McKee, S.: Stability of numerical schemes on staggered grids. (2008)
  15. Sousa, F. S.; Castelo, A.; Nonato, L. G.; Mangiavacchi, N.; Cuminato, J. A.: Local volume-conserving free surface smoothing (2007)
  16. Raad, Peter E.; Bidoae, Razvan: The three-dimensional Eulerian--Lagrangian marker and micro cell method for the simulation of free surface flows (2005)
  17. de Sousa, F. S.; Mangiavacchi, N.; Nonato, L. G.; Castelo, A.; Tomé, M. F.; Ferreira, V. G.; Cuminato, J. A.; McKee, S.: A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces (2004)
  18. Ferreira, V. G.; Tomé, M. F.; Mangiavacchi, N.; Castelo, A.; Cuminato, J. A.; Fortuna, A. O.; McKee, S.: High-order upwinding and the hydraulic jump (2002)
  19. Tomé, M. F.; Filho, A. C.; Cuminato, J. A.; Mangiavacchi, N.; McKee, S.: \textttGENSMAC3D: A numerical method for solving unsteady three-dimensional free surface flows. (2001)