# A distributed Lagrange multiplier/fictitious domain method for particulate flows

@article{Glowinski1999ADL, title={A distributed Lagrange multiplier/fictitious domain method for particulate flows}, author={Roland Glowinski and Tsorng-Whay Pan and Todd I. Hesla and DanielD. Joseph}, journal={International Journal of Multiphase Flow}, year={1999}, volume={25}, pages={755-794} }

Abstract A new Lagrange-multiplier based fictitious-domain method is presented for the direct numerical simulation of viscous incompressible flow with suspended solid particles. The method uses a finite-element discretization in space and an operator-splitting technique for discretization in time. The linearly constrained quadratic minimization problems which arise from this splitting are solved using conjugate-gradient algorithms. A key feature of the method is that the fluid–particle motion…

## Figures from this paper

## 997 Citations

A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows

- Physics
- 2000

Abstract A distributed Lagrange multiplier/fictitious domain method (DLM) is developed for simulating the motion of rigid particles suspended in the Oldroyd-B fluid. This method is a generalization…

A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows

- Physics
- 2000

A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct numerical simulation of rigid particulate flows in a Newtonian fluid was presented previously. An important feature of this…

A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow

- Mathematics
- 2000

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…

A Fictitious Domain Method with Distributed Lagrange Multiplier for Particulate Flow

- Mathematics
- 2007

In this paper, a numerical simulation of the incompressible viscous flow around a lot of blowing particles is presented. The rigid particle motions in the fluid are caused by fluid and gravity…

Direct Simulations of 2 D Fluid – Particle Flows in Biperiodic Domains

We propose a method to simulate the motion of 2D rigid particles in a viscous, incompressible fluid. Within the Arbitrary Lagrangian Eulerian framework, momentum equations for both the fluid and the…

A fictitious domain method with distributed Lagrange multipliers for the numerical simulation of par

- Mathematics
- 1998

The main goal of this article, which generalizes [4] considerably, is to discuss the numerical simulation of particulate flow for mixtures of incompressible viscous fluids and rigid particles. Such…

A hybrid FD-DEM solver for rigid particles in viscous fluid

- Physics
- 2015

Abstract In this article, the dynamics of colliding particles immersed in a viscous fluid is numerically investigated. An improved fictitious domain (FD) method for a solid–fluid system is developed…

Regular Article: Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains

- Mathematics
- 1999

We propose a method to simulate the motion of 2D rigid particles in a viscous, incompressible fluid. Within the arbitrary Lagrangian Eulerian framework, momentum equations for both the fluid and the…

Floating Particles

- 2003

A finite element code based on the level set and distributed Lagrange multiplier (DLM) methods is developed for simulating the motion of rigid spherical particles on two-fluid interfaces. The…

An Improved Fictitious Domain Method for Simulating Sedimenting Rigid Particle in a Viscous Fluid

- Computer ScienceParCo 2013
- 2013

An improved fictitious domain–based computational method for a solid-fluid system is developed and a collision strategy for multiple particles is presented and a direct-forcing domain method is applied for simulation of multi-particle fluid flows.

## References

SHOWING 1-10 OF 79 REFERENCES

Direct simulation of flows of solid-liquid mixtures

- Physics
- 1996

Abstract A finite element technique based on moving unstructured grids is developed to simulate the motion of a large number of solid particles in a flowing liquid. A generalized Galerkin finite…

A three-dimensional fictitious domain method for incompressible fluid flow problems

- Mathematics
- 1997

A new Galerkin finite element method for the solution of the Navier–Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element…

A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori

- Mathematics
- 1997

Abstract We describe in this Note a method for the numerical simulation of incompressible viscous flow around moving rigid bodies; we suppose the rigid body motions a priori known. The computational…

Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies

- Mathematics
- 1998

Abstract In this article we discuss the application of a distributed Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modelled by the…

Direct simulation of fluid particle motions

- Physics
- 1992

Continuum models of two-phase flows of solids and liquids use constitutive assumptions to close the equations. A more fundamental approach is a “molecular dynamic” simulation of flowing “big”…

A front-tracking method for viscous, incompressible, multi-fluid flows

- Mathematics
- 1992

Abstract A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is…

Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 1997

A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented and an implicit quasi-Newton method is developed that allows reasonable time steps to be used.

FINITE ELEMENT METHODS FOR NAVIER-STOKES EQUATIONS

- Physics
- 1992

The main goal of this article is to address the finite element solution of the Navier-Stokes equations modeling compressible and incompressible viscous flow. It is the opinion of the authors that…

A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations

- Mathematics
- 1994

In this article we discuss a fictitious domain method for the numerical solutions of three-dimensional elliptic problems with Dirichlet boundary conditions and also of the Navier-Stokes equations…

A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow

- Mathematics
- 1997

Abstract In this Note we describe a novel method for the solution of the Navier-Stokes equations for incompressible viscous fluids. This method, which can be viewed as an alternative to the methods…