Numerical Methods Coupling Discrete Particles to a Continuum
A collection of particles “talking” to their surroundings:
Physical systems comprising a dispersed collection of particles in continuous media (fluid/solid) involve two-way exchange of mass/momentum/energy. Under certain conditions, these two-way interactions do not appreciably affect the overall continuum behavior – e.g. sparsely populated small particles in a large fluid domain does not change flow behavior. When relevant, the resolution of these two-way interactions can be computationally demanding, and in many cases leads to complex numerical systems requiring special techniques. On the one hand Stokesian, on the other hand FSI. On the one hand mesh-based, on the other hand point sources. A long-term goal of my research is to investigate numerical method development for unsteady two-way and four-way coupled particle systems.
Physical systems comprising a dispersed collection of particles in continuous media (fluid/solid) involve two-way exchange of mass/momentum/energy. Under certain conditions, these two-way interactions do not appreciably affect the overall continuum behavior – e.g. sparsely populated small particles in a large fluid domain does not change flow behavior. When relevant, the resolution of these two-way interactions can be computationally demanding, and in many cases leads to complex numerical systems requiring special techniques. On the one hand Stokesian, on the other hand FSI. On the one hand mesh-based, on the other hand point sources. A long-term goal of my research is to investigate numerical method development for unsteady two-way and four-way coupled particle systems.
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Fictitious domain numerical methods:
For collections of particles within a domain with complex geometry, and undergoing collisions, generating good quality meshes that resolve the particle boundaries is a major hurdle. Numerical techniques that “embed” the particle within a background mesh of the overall domain avoid the complication of explicit tracking of particle boundaries, providing a suitable alternative. Fictitious domain and Immersed boundary methods are two prominent examples of such techniques. One of my ongoing research focus is on developing efficient fictitious domain methods for unsteady particle laden-flow, with specific interest in cardiovascular/physiological flows. In particular, I have developed a fictitious domain based framework for modeling the interaction of a blood clot with blood flow. (read more here). I am currently also employing fictitious domain methods to investigate porous media flows and the role of pore-microstructure variations on the flow properties. |
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Two-way coupling of discrete particles to a fluid/solid:
Under certain conditions (e.g. small particle size, dilute systems etc.) the two-way coupled interactions can be resolved by imposing mass/momentum/energy sources at the locations of the particles in the domain. This, of course, is complementary to methods that explicitly or weakly resolve the boundaries. I have devised point-source based techniques to couple the impingement of a granular jet on a substrate to stresses and deformation within the substrate material, using semi-analytical solutions for point contact loading and stress. For fluid-particle coupling, I used a similar technique to study transport of fragmented clots in human carotid artery. |