In this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies. The simulation methods rest essentially on the combination of: (a) Lagrange-multiplier-based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region. (b) Finite element approximations of the Navier-Stokes equations occurring in the global model. (c) Time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model. The above methodology is particularly well suited to the direct numerical simulation of particulate flow, such as the flow of mixtures of rigid solid particles and incompressible viscous fluids, possibly non-Newtonian. We conclude this article with the presentation of the results of various numerical experiments, including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions.
Bibliographical noteFunding Information:
We acknowledge the helpful comments and suggestions of E. J. Dean, V. Girault, J. He, Y. Kuznetsov, Yong-Jun Lin, G. Rodin, A. Sameh, V. Sarin, and P. Singh, and also the support of the Supercomputing Institute at the University of Minnesota concerning the use of an SGI Origin 2000. We acknowledge also the support of the NSF (Grants ECS-9527123, CTS-9873236, and DMS-9973318) and Dassault Aviation. The assistance of P. Muscarello is also acknowledged.
- Distributed Lagrange multipliers
- Fictitious domain methods
- Finite element methods
- Liquid-solid mixtures
- Navier-Stokes equations
- Particulate flow
- Rayleigh-Taylor instabilities
- Store separation