This Note presents a new method of direct forcing to deal with obstacles in incompressible flows. It mixes projection schemes and velocity penalty schemes. The penalized direct forcing term is distributed in the velocity prediction and the correction equations. It leads to a natural treatment in the correction equation of the boundary conditions in pressure around obstacles. A numerical experiment provided an illustration of the method.
Cette Note présente une nouvelle méthode de forçage directe pour prendre en compte des obstacles dans un écoulement incompressible. Elle mélange méthodes de projection et de pénalisation des vitesses. La ventilation du terme de forçage direct pénalisé dans les équations de prédiction et de correction conduit à un traitement naturel des conditions aux limites pour la correction de pression aux bords des obstacles. Une expérience numérique est présentée à titre d'illustration.
Accepted:
Published online:
Michel Belliard 1; Clarisse Fournier 2
@article{CRMATH_2010__348_19-20_1133_0, author = {Michel Belliard and Clarisse Fournier}, title = {Penalized direct forcing and projection schemes for {Navier{\textendash}Stokes}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1133--1136}, publisher = {Elsevier}, volume = {348}, number = {19-20}, year = {2010}, doi = {10.1016/j.crma.2010.09.016}, language = {en}, }
TY - JOUR AU - Michel Belliard AU - Clarisse Fournier TI - Penalized direct forcing and projection schemes for Navier–Stokes JO - Comptes Rendus. Mathématique PY - 2010 SP - 1133 EP - 1136 VL - 348 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2010.09.016 LA - en ID - CRMATH_2010__348_19-20_1133_0 ER -
Michel Belliard; Clarisse Fournier. Penalized direct forcing and projection schemes for Navier–Stokes. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1133-1136. doi : 10.1016/j.crma.2010.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.016/
[1] A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math., Volume 81 (1999), pp. 497-520
[2] Numerical solution of the Navier–Stokes equations, Math. Comp., Volume 22 (1968), pp. 745-762
[3] Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., Volume 161 (2000), pp. 35-60
[4] An unconditionally stable pressure correction scheme for the compressible barotropic Navier–Stokes equations, M2AN Math. Model. Numer. Anal., Volume 42 (2008), pp. 303-331
[5] Finite-difference immersed boundary method consistent with wall conditions for incompressible turbulent flow simulations, J. Comput. Phys., Volume 226 (2007), pp. 1485-1508
[6] Une méthode de pénalité-projection pour les écoulements dilatables, European J. Comput. Mech., Volume 17 (2008), pp. 453-480
[7] J. Mohd-Yusof, Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries, CTR Annual Research Briefs, NASA Ames/Stanford University, 1997.
[8] Numerical analysis of blood flow in heart, J. Comput. Phys., Volume 25 (1977), pp. 220-252
[9] On error estimates of some higher order projection and penalty-projection methods for Navier–Stokes equations, Numer. Math., Volume 62 (1992), pp. 49-73
[10] Sur l'approximation de la solution des équations de Navier–Stokes par la méthode des pas fractionnaires, Arch. Ration. Mech. Anal., Volume 32 (1969), pp. 135-153
Cited by Sources:
Comments - Politique