Abstract
Proteus1 is a new code that utilizes elements of the Immersed Boundary (IB) and Lattice Boltzmann Method (LBM) as well as a Direct Forcing (DF) scheme. As a computational method, it is very flexible and it appears to be ideal in solving fluid-particle interaction problems including problems with deformable boundaries. Proteus uses a regular Eulerian grid for the flow domain and a regular Lagrangian grid to follow particles that are contained in the flow field. The rigid body conditions for the fluid and the particles are enforced by applying the external force acting on the boundary of particles. A penalty method is used, which assumes that the particle boundary is deformable with a high stiffness constant. The velocity fields for the fluid and particles are solved by incorporating a force density term into the lattice Boltzmann equation. This force term is determined by using a technique that is based on the direct forcing scheme. Proteus preserves all the advantages of LBM in tracking a group of particles and, at the same time, provides an alternative and better approach to treating the solid-fluid boundary conditions. Because of this it provides for a smooth boundary interface, with only a few nodes assigned for the size of particles. This new method also solves the problems of fluctuation of the forces and velocities on the particles when the “bounceback” boundary conditions are applied. The method has the capability to simulate deformable particles and fluid-structure deformation. The results of the Proteus code have been validated by comparison with results from other computational methods as well as experimental data. Some of the validation results will be given in the presentation of this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Feng, Z.-G. and Michaelides, E.E., 2002, Inter-particle forces and lift on a particle attached to a solid boundary in suspension flow, Phys. Fluids 14, 49–60.
Feng, Z.-G. and Michaelides, E.E., 2004, An immersed boundary method combined with lattice Boltzmann method for solving fluid and particles interaction problems, J. Comput. Phys. 195, 602–628.
Feng, Z.G. and Michaelides, E.E., 2005, Proteus — A direct forcing method in the simulation of particulate flows, J. Comput. Phys. 202, 20–51.
Glowinski, R., Pan, T.-W., Hesla, T.I. and Joseph, D.D., 1999, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25, 755–794.
Glowinski, R., Pan, T.-W., Hesla, T.I., Joseph, D.D. and Periaux, J., 2001, A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys. 169, 363–426.
Goldstein, D., Handler, R. and Sirovich, L., 1993, Modeling a no-slip flow boundary with an external force field, J. Comput. Phys. 105, 354–366.
Höfler, K. and Schwarzer, S., 2000, Navier—Stokes simulation with constraint forces: Finite-difference method for particle-laden flows and complex geometries, Phys. Rev. E 61, 7146–7160.
Ladd, A.J.C., 1994, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation, J. Fluid Mech. 271, 285–310.
Ladd, A.J.C., 1994, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part II. Numerical results, J. Fluid Mech. 271, 311–339.
Mohd-Yusof, J., 1997, Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries, Annual Research Briefs, Center for Turbulence Research, Stanford University.
Peskin, C.S., 1977, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25, 220–252.
Peskin, C.S., 2002, The immersed boundary method, Acta Numerica 11, 479–517.
Ten Cate, A., Nieuwstad, C.H., Derksen J.J. and Van den Akker, H.E.A., 2002, Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. Fluids 14, 4012–4025.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Feng, ZG., Michaelides, E.E. (2006). Proteus—A New Computational Scheme for Deformable Particles and Particle Interaction Problems. In: Balachandar, S., Prosperetti, A. (eds) IUTAM Symposium on Computational Approaches to Multiphase Flow. Fluid Mechanics and Its Applications, vol 81. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4977-3_16
Download citation
DOI: https://doi.org/10.1007/1-4020-4977-3_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4976-7
Online ISBN: 978-1-4020-4977-4
eBook Packages: EngineeringEngineering (R0)