Conservation under Incompatibility for Fluid-Solid-Interaction Problems: the NPCL Method
Summary
Finite-element discretizations of fluid-solid-interaction problems only trivially preserve the conservation properties of the underlying problem under restrictive compatibility conditions on the approximation spaces for the fluid and the solid. The present work introduces a new general method for enforcing interface conditions that maintains the conservation properties under incompatibility. The method is based on a nonlinear variational projection of the velocity field to impose the kinematic condition, and a consistent evaluation of the load functional that accounts for the dynamic condition. Numerical results for a projection problem are presented to illustrate the properties of the method.
Keywords
fluid-solid interaction incompatibility conservation space-time finite-element methods.Preview
Unable to display preview. Download preview PDF.
References
- 1.E.D. Bloch. A First Course in Geometric Topology and Differential Geometry. Birkhäuser, Boston, 1996.Google Scholar
- 2.E.H. van Brummelen. Mesh association by projection along smoothed-normal-vector fields: association of closed manifolds. 2006. Accepted for publication in Int. J. Num. Meth. Engng. Also available as DACS report DACS-06-005 at http://www.emserver.lr.tudelft.nl/downloads/DACS-06-005.pdf.
- 3.C. Farhat, M. Lesoinne, and P. LeTallec. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Engrg., pages 95–114, 1998.Google Scholar
- 4.X. Jiao and M.T. Heath. Common-refinement-based data transfer between non-matching meshes in multiphysics simulations. Int. J. Numer. Meth. Engng., 61:2402–2427, 2004.MATHCrossRefMathSciNetGoogle Scholar
- 5.J.L. Lions and E. Magenes. Non-Homogeous Boundary Value Problems and Applications I. Springer-Verlag, 1972.Google Scholar
- 6.J.T. Oden and J.N. Reddy. An Introduction to the Mathematical Theory of Finite Elements. Pure and Applied Mathematics. John Wiley & Sons, New York, 1974.Google Scholar
- 7.R.W. Ogden. Non-linear elastic deformations. Ellis Horwood, 1984.Google Scholar
- 8.J. Salençon. Handbook of Continuum Mechanics. Springer-Verlag, Heidelberg, 2001.MATHGoogle Scholar
- 9.R. Temam and A. Mirainville. Mathematical Modeling in Continuum Mechanics. Cambridge University Press, 2001.Google Scholar
- 10.P. Wesseling. Principles of Computational Fluid Dynamics, volume 29 of Springer Series in Computational Mathematics. Springer, Berlin, 2001.Google Scholar
- 11.E. Zeidler. Applied Functional Analysis: Applications to Mathematical Physics, volume 108 of Applied Mathematical Sciences. Springer, Berlin, 1995.Google Scholar