The aim of this study was to develop a numerical model to simulate the surface erosion occurring at a fluid/soil interface subject to a flow process. We used a penalization procedure to compute flow around obstacles. A fictitious domain method allowed the use of fast and efficient finite volumes approximations on Cartesian meshes and avoided unstructured body-fitted meshes. The water/soil interface evolution was described with a Level Set function. Several numerical simulations confirmed the model's ability to predict the interfacial erosion of soils.
Accepted:
Published online:
Frédéric Golay 1, 2; Damien Lachouette 1, 2; Stéphane Bonelli 2; Pierre Seppecher 1
@article{CRMECA_2010__338_6_333_0, author = {Fr\'ed\'eric Golay and Damien Lachouette and St\'ephane Bonelli and Pierre Seppecher}, title = {Interfacial erosion: {A} three-dimensional numerical model}, journal = {Comptes Rendus. M\'ecanique}, pages = {333--337}, publisher = {Elsevier}, volume = {338}, number = {6}, year = {2010}, doi = {10.1016/j.crme.2010.06.001}, language = {en}, }
TY - JOUR AU - Frédéric Golay AU - Damien Lachouette AU - Stéphane Bonelli AU - Pierre Seppecher TI - Interfacial erosion: A three-dimensional numerical model JO - Comptes Rendus. Mécanique PY - 2010 SP - 333 EP - 337 VL - 338 IS - 6 PB - Elsevier DO - 10.1016/j.crme.2010.06.001 LA - en ID - CRMECA_2010__338_6_333_0 ER -
Frédéric Golay; Damien Lachouette; Stéphane Bonelli; Pierre Seppecher. Interfacial erosion: A three-dimensional numerical model. Comptes Rendus. Mécanique, Volume 338 (2010) no. 6, pp. 333-337. doi : 10.1016/j.crme.2010.06.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.06.001/
[1] Soil erosion in the boundary layer flow along a slope: A theoretical study, Eur. J. Mech. B Fluids, Volume 26 (2007), pp. 707-719
[2] The scaling law in the hole erosion test with a constant pressure drop, Internat. J. Numer. Methods Engrg., Volume 32 (2008), pp. 1573-1595
[3] One-dimensional modeling of piping flow erosion, C. R. Mecanique, Volume 336 (2008), pp. 731-736
[4] A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math., Volume 81 (1999), pp. 497-520
[5] Assessing embankment dam filters that do not satisfy design criteria, J. Geotech. Geoenviron. Eng., Volume 125 (2001) no. 7, pp. 398-407
[6] Investigation of rate of erosion of soils in embankment dams, J. Geotech. Geoenviron. Eng., Volume 130 (2004) no. 4, pp. 373-380
[7] Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows, Math. Methods Appl. Sci., Volume 22 (1999), pp. 1395-1412
[8] A fictitious domain/finite element method for particulate flows, J. Comput. Phys., Volume 192 (2003), pp. 105-123
[9] Fictitious domain approach for numerical modelling of Navier–Stokes equations, Internat. J. Numer. Methods Fluids, Volume 34 (2000), pp. 651-684
[10] Fronts propagating with curvature dependent speed: Algorithm for tracking material interface, J. Comput. Phys., Volume 39 (1981), pp. 201-225
[11] A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comput. Phys., Volume 124 (1996), pp. 449-464
[12] A conservative level set method for two phase flow, J. Comput. Phys., Volume 210 (2005), pp. 225-246
[13] A level set approach for computing solutions to incompressible two-phase flows, J. Comput. Phys., Volume 114 (1994), pp. 146-159
[14] Level-set, penalization and Cartesian meshes: A paradigm for inverse problems and optimal design, J. Comput. Phys., Volume 228 (2009), pp. 6291-6315
[15] Numerical calculation of time dependent viscous incompressible flow with free surface, Phys. Fluids, Volume 8 (1965) no. 12, pp. 2182-2189
[16] Computation of flow past complex geometries using MAC algorithm on body-fitted coordinates, Eng. Appl. Comput. Fluids Mech., Volume 3 (2009) no. 1, pp. 15-27
[17] A one-cell local multigrid method for solving unsteady incompressible multiphase flows, J. Comput. Phys., Volume 163 (2000), pp. 172-215
[18] On stability condition for bifluid flows with surface tension: Application to microfluidics, J. Comput. Phys., Volume 227 (2008), pp. 6140-6164
[19] Weighted ENO schemes for Hamilton–Jacobi equations, J. Sci. Comput., Volume 21 (2000) no. 6, pp. 2126-2143
[20] Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., Volume 175 (2002), pp. 200-224
[21] Numerical schemes for low Mach wave breaking, Int. J. Comput. Fluid Dyn., Volume 21 (2007) no. 2, pp. 69-86
Cited by Sources:
Comments - Policy