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

A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct n umerical simulation of rigid particulate flows in a Newtonian fluid was pre sented previously. An important feature of this finite element based method is that the flow in the particle domain is constrained to be a rigid body motion by using a well-chosen field of Lagrange multipliers. The constraint of rigid body motion is represented by u = U + omega x r; u being the velo city of the fluid at a point in the particle domain; U and omega are the tr anslational and angular velocities of the particle, respectively; and r is the position vector of the point with respect to the center of mass of the particle. The fluid-particle motion is treated implicitly using a combined weak formulation in which the mutual forces cancel. This formulation togeth er with the above equation of constraint gives an algorithm that requires e xtra conditions on the space of the distributed Lagrange multipliers when t he density of the fluid and the particles match. In view of the above issue a new formulation of the DLM for particulate flow is presented in this pap er. In this approach the deformation rate tensor within the particle domain is constrained to be zero at points in the fluid occupied by rigid solids. This formulation shows that the state of stress inside a rigid body depend s on the velocity field similar to pressure in an incompressible fluid. The new formulation is implemented by modifying the DLM code for two-dimension al particulate flows developed by others. The code is verified by comparing results with other simulations and experiments. (C) 2000 Elsevier Science Ltd. All rights reserved.