Numerical modeling of suffusion as an interfacial erosion process

6. References

• Angot , P. , Bruneau , C.-H. and Fabrie , P. 1999 . “A penalization method to take into account obstacles in incompressible viscous flows” . Numer. Math. , 81 : 497 – 520 .
   Web of Science ®Google Scholar
• Angot , P. 1999 . “Analysis of Singular Perturbations on the Brinkman Problem for Fictitious Domain Models of Viscous Flows” . Math. Meth. Appl. Sci , 22 : 1395 – 1412 .
   Web of Science ®Google Scholar
• Bonelli , S. and Brivois , O. 2008 . “The scaling law in the hole erosion test with a constant pressure drop” . Int. J. Num. Meth. Eng. , 32 : 1573 – 1595 .
   Google Scholar
• Bost , C. , Cottet , G.-H. and Maitre , E. 2010 . “Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid” . SIAM J. Numer. Anal , 48 ( n° 4 ) : 1313 – 1337 .
   Web of Science ®Google Scholar
• Bouddour , A. , Auriault , J. L. and Mhamdi-Alaoui , M. 1996 . “Erosion and deposition of solid particles in porous media: Homogenization analysis of a formation damage” . Transport Porous Med , 25 ( n° 2 ) : 121 – 146 .
   Web of Science ®Google Scholar
• Brivois , O. , Bonelli , S. and Borghi , R. 2007 . “Soil erosion in the boundary layer flow along a slope: a theoretical study” . Eur. J. Mech. B-Fluid , 26 : 707 – 719 .
   Web of Science ®Google Scholar
• Chang , Y. C. , Hou , T. Y. , Merriman , B. and Osher , S. 1996 . “A Level-set formulation of eulerian interface capturing methods for incompressible fluid flows” . J. Comput. Phys. , 124 : 449 – 464 .
   Web of Science ®Google Scholar
• Chantalat , F. , Bruneau , C. H. , Galusinski , C. and Iollo , A. 2009 . “Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design” . J. Comput. Phys. , 228 : 6291 – 6315 .
   Web of Science ®Google Scholar
• Chauchat , J. and Médale , M. 2010 . “A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow” . Comput. Methods Appl. Mech. Engrg , 199 ( n° 9–12 ) : 439 – 449 .
   Web of Science ®Google Scholar
• Diaz-Goano , C. , Minev , P. D. and Nandakumar , K. 2003 . “A fictitious domain/finite element method for particulate flows” . J. Comput. Phys. , 192 : 105 – 123 .
   Web of Science ®Google Scholar
• Fell , R. and Fry , J.-J. 2007 . Internal Erosion of Dams and their Foundations London : Taylor & Francis .
   Google Scholar
• Fortin , M. and Glowinski , R. 1983 . “Augmented lagrangian methods: applications to the numerical solution of boundary-value problems” . In studies in mathematics and its applications North-Holland , , Amsterdam vol. 15
   Google Scholar
• Galusinski , C. and Vigneaux , P. 2008 . “On stability condition for bifluid flows with surface tension: application to microfluidics” . J. Comput. Phys. , 227 : 6140 – 6164 .
   Web of Science ®Google Scholar
• Guus , S. , Kees , V. and Kees , K. 1994 . “On the implementation of symetric and antisymetric periodic boundary conditions for incompressible flow” . Int. J. Num. Meth. Fluids , 18 : 1153 – 1165 .
   Web of Science ®Google Scholar
• Gutiérrez , F. , Guerrero , J. and Lucha , P. 2008 . “A genetic classification of sinkholes illustrated from evaporate paleokarst exposures in Spain” . Environ. Geol. , 53 ( n° 5 ) : 993 – 1006 .
   Web of Science ®Google Scholar
• Golay , F. , Lachouette , D. , Bonelli , S. and Seppecher , P. 2010 . “Interfacial erosion: A three-dimensional numerical model” . C.R. Mecanique , 338 ( n° 6 ) : 333 – 337 .
   Web of Science ®Google Scholar
• Golay , F. , Lachouette , D. , Bonelli , S. and Seppecher , P. 2011 . “Numerical modelling of interfacial soil erosion with viscous incompressible flows” . Comput. Methods Appl. Mech. Engrg , 200 ( n° 1:4 ) : 383 – 391 .
   Web of Science ®Google Scholar
• Harlow , F. H. and Welsh , J. E. 1965 . “Numerical calculation of time dependent viscous incompressible flow with free surface” . Phys. Fluids , 8 ( n° 12 ) : 2182 – 2189 .
   Web of Science ®Google Scholar
• Jiang , G. S. and Peng , D. 2000 . “Weighted ENO schemes for Hamilton-Jacobi equations” . J. Sci. Comput , 21 ( n° 6 ) : 2126 – 2143 .
   Web of Science ®Google Scholar
• Khadra , K. , Angot , P. , Parneix , S. and Caltagirone , J. P. 2000 . “Fictitious domain approach for numerical modelling of Navier-Stokes equations” . Int. J. Numer. Meth. Fluids , 34 : 651 – 684 .
   Web of Science ®Google Scholar
• Lachouette , D. , Golay , F. and Bonelli , S. 2008 . “One-dimensional modeling of piping flow erosion” . C. R. Mecanique , 336 : 731 – 736 .
   Web of Science ®Google Scholar
• Olson , E. and Kreiss , G. 2005 . “A conservative level-set method for two phase flow” . J. Comput. Phys. , 210 : 225 – 246 .
   Web of Science ®Google Scholar
• Osher , S. and Sethian , J. 1981 . “A., Fronts propagating with curvature-dependent speed: Algorithms for tracking material interface” . J. Comp. Phys. , 39 : 201 – 225 .
   Google Scholar
• Papamichos , E. , Vardoulakis , I. and Tronvoll , J. Skjaerstein . 2001 . “A Volumetric sand production model and experiment” . Int. J. Num. Anal. Meth. , 25 : 789 – 808 .
   Web of Science ®Google Scholar
• Prodanovic , M. and Bryant , S. 2006 . “A level-set method for determining critical curvatures for drainage and imbibition” . J. ColloidInterf. Sci. , 304 : 442 – 458 .
   Google Scholar
• Ramiere , I. , Angot , P. and Belliard , M. 2007 . “A fictitious domain approach with spread interface for elliptic problems with general boundary conditions” . Comput. Methods Appl. Mech. Engrg. , 196 ( n° 4–6 ) : 766 – 781 .
   Web of Science ®Google Scholar
• Sterpi , D. 2003 . “Effects of the erosion and transport of fine particles due to seepage flow” . international journal of Geomechanics , 3 ( n° 2 ) : 111 – 122 .
   Google Scholar
• Sussman , M. , Smereka , P. and Osher , S. 1994 . “A level-set approach for computing solutions to incompressible two-phase flows” . J. Comput. Phys. , 114 : 146 – 159 .
   Web of Science ®Google Scholar
• Vardoulakis , I. , Stavropoulou , M. and Papanstasiou , P. 1996 . “Hydromechanical aspects of sand production problem” . Transport in Porous Med , 22 : 225 – 244 .
   Web of Science ®Google Scholar
• Vardoulakis , I. , Papanastasiou , P. and Stavropoulou , M. 2001 . “Sand Erosion in Axial Flow Conditions” . Transport Porous Med , 45 : 267 – 281 .
   Web of Science ®Google Scholar
• Vincent , S. , Caltagirone , J. P. , Lubin , P. and Randrianarivelo , T. N. 2004 . “An adaptative augmented Lagrangian method for three-dimensional multimaterial flows” . Comput. Fluids , 33 ( n° 10 ) : 1273 – 1289 .
   Web of Science ®Google Scholar