Grant: Discovery Grants Program - Individual

Particle-based methods are a popular simulation tool that provide a more refined system dynamics with the ability to capture and explore system dynamics that cannot be modeled by differential equations. Recent technological advances have allowed for applications of particle-based methods to a wide array of problems including particle-based flow models and biochemical networks. Recent results in applying particle-based methods to simulate flow through a local constriction have shown the compressible nature of the particle-based method. Care must be taken to control and to minimize this effect when simulating flows for incompressible, or weakly compressible, fluids such as blood. Realistic flow domains for blood flow, such as flow through a constricted artery, or flow through a branched vessel naturally give rise to compressibility effects that need to be quantified and controlled for this particular application. On the other hand, the built-in compressibility is ideal for exploring a range of compressible flow problems including microfluidics. Additionally, incorporation of reactions into the particle-based method allows for the study of reactive or multiphase flow applications, as well as for simulating spatially distributed biochemical networks such as the chemotactic response of an E. coli cell for example.******The following novel work will be carried out in this research program: Development of numerical and analytical techniques to quantify compressibility and slip in complex flow geometries; development of numerical techniques for multiparticle collision dynamics (MPCD) flow through domains with porous walls; development of reactive MPCD simulations of reactive or multiphase flow and biochemical networks; development of analytical and numerical techniques for compressible flow problems.******Compressibility effects have recently been observed when using particle-based methods to simulate flow through a local constriction, as well as non-equilibrium effects. Making use of the built-in compressibility in MPCD flow, a number of numerical and theoretical investigations will be carried out in order to quantify and control the compressibility if desired. The research program will lead to important contributions in: flows of chemically reactive media for which low concentration chemical species exist, compressible flows, improved numerical/theoretical estimates for viscosity expressions in MPCD flow in non-equilibrium conditions, MPCD flow through complex flow domains with applications to blood flow and microfluidics, and numerical simulations of biologically relevant biochemical networks. The HQP trained under this program will obtain highly desirable mathematical modeling skills, programming experience, dissemination experience, and refereed journal publications, which are highly desirable skills/milestones for industry and academia alike.**