In this article we discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier-Stokes equations around moving rigid bodies; the rigid body motion is due to hydrodynamical forces and gravity. The solution method combines finite element approximations, time discretization by operators splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method. We conclude this article by the presentation of numerical results concerning the simulation of an incompressible viscous flow around a NACA0012 airfoil with a fixed center, but free to rotate, then the sedimentation of circular cylinders in 2-D channels, and finally the sedimentation of spherical balls in cylinders with square cross-sections. (C) 2000 Elsevier Science S.A. All rights reserved.
|Original language||English (US)|
|Number of pages||27|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Apr 14 2000|
Bibliographical noteFunding Information:
We acknowledge the helpful comments and suggestions of E.J. Dean, V. Girault, J. He, Y. Kuznetsov, B. Maury, and G. Rodin and also the support of NEC concerning the use of an SX-3 supercomputer. We acknowledge also the support of the NSF under HPCC Grand Challenge Grant ECS-9527123, NSF (Grants DMS 8822522, DMS 9112847, DMS 9217374), Dassault Aviation, DRET (Grant 89424), DARPA (Contracts AFOSR F49620-89-C-0125, AFOSR-90-0334), the Texas Board of Higher Education (Grants 003652156ARP and 003652146ATP) and the University of Houston (PEER grant 1-27682).
- Fictitious domain methods
- Liquid-solid mixtures
- Navier-Stokes equations
- Particulate flow
- Rayleigh-Taylor instabilities