Publications

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We performed an investigation into explicit algorithms for the simulation of incompressible flows using methods with a finite, but small amount of compressibility added. Such methods include the artificial compressibility method and the lattice-Boltzmann method. The impetus for investigating such techniques stems from the increasing use of parallel computation at all levels (processors, clusters, and graphics processing units). Explicit algorithms have the potential to leverage these resources. In our investigation, a new form of artificial compressibility was derived. This method, referred to as the Entropically Damped Artificial Compressibility (EDAC) method, demonstrated superior results to traditional artificial compressibility methods by damping the numerical acoustic waves associated with these methods. Performance nearing that of the lattice- Boltzmann technique was observed, without the requirement of recasting the problem in terms of particle distribution functions; continuum variables may be used. Several example problems were investigated using a finite-di erence and finite-element discretizations of the EDAC equations. Example problems included lid-driven cavity flow, a convecting Taylor-Green vortex, a doubly periodic shear layer, freely decaying turbulence, and flow over a square cylinder. Additionally, a scalability study was performed using in excess of one million processing cores. Explicit methods were found to have desirable scaling properties; however, some robustness and general applicability issues remained.

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We use a recently developed hybrid numerical technique [MacMeccan et al. (2009)] that combines a lattice-Boltzmann (LB) fluid solver with a finite element (FE) solid-phase solver to study suspensions of elastic capsules. The LB method recovers the Navier-Stokes hydrodynamics, while the linear FE method models the deformation of fluid-filled elastic capsules for moderate levels of deformation. The simulation results focus on accurately describing the suspension rheology, including the particle pressure, and relating these changes to changes in the microstructure. Simulations are performed with hundreds of particles in unbounded shear allowing an accurate description of the bulk suspension rheology and microstructure. In contrast to rigid spherical particles, elastic capsules are capable of producing normal stresses in the dilute limit. For dense suspensions, the first normal stress difference is of particular interest. The first normal stress difference, which is negative for dense rigid spherical suspensions, undergoes a sign change at moderate levels of deformation of the suspended capsules.

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