The Sparse Cardinal Sine Decomposition applied to Stokes integral equations

François Alouges (1) , Matthieu Aussal (1) , Aline Lefebvre-Lepot (1) , Franck Pigeonneau (2) , Antoine Sellier (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 SVI - Surface du Verre et Interfaces
3 LadHyX - Laboratoire d'hydrodynamique

Numerical simulations of two-phase flows driven by viscosity (e.g. for bubble motions in glass melting process) rely on the ability to efficiently compute the solutions to discretized Stokes equations. When using boundary element methods to track fluid interfaces, one usually faces the problem of solving linear systems with a dense matrix with a size proportional to the system number of degrees of freedom. Acceleration techniques, based on the compression of the underlying matrix and efficient matrix vector products are known (Fast Multipole Method, H-matrices, etc.) but are usually rather cumbersome to develop. More recently, a new method was proposed, called the " Sparse Cardinal Sine Decomposition " , in the context of acoustic problems to tackle this kind of problem in some generality (in particular with respect to the Green kernel of the problem). The proposed contribution aims at showing the potential applicability of the method in the context of viscous flows governed by Stokes equations.

Mots clés: Stokes equations; Boundary Element Method; Fast Multipole Method

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

François Alouges, Matthieu Aussal, Aline Lefebvre-Lepot, Franck Pigeonneau, Antoine Sellier. The Sparse Cardinal Sine Decomposition applied to Stokes integral equations. ICMF-2016 – 9th International Conference on Multiphase Flow, May 2016, Florence, Italy. ⟨hal-01323556⟩