Computational Methods for the Direct Simulation of Particulate Flow of Newtonian and Non-Newtonian Incompressible Viscous Fluids

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9973318The main goal of this project is to address the numerical solution of the Navier-Stokes equations modeling the flow of incompressible Newtonian and non-Newtonian viscous fluids and to combine the resulting methodology with appropriate domain embedding methods to investigate the simulation of particulate incompressible viscous fluid flows, e.g., flow of mixtures of incompressible fluids and solid particles moving, typically, under the effect of gravity and hydrodynamical forces. The numerical methodology will rely on the following basic basic ingredients:(1) Time discretization by operator splitting,(2) Treatment of advection by the method of characteristics or reduction to a second order wave-like equation,(3) Space approximation by finite elements,(4) Use of a distributed Lagrange multiplier/fictitious (embedding) domain methodology to localize the solid particles and force their rigid body motion.Typical non-Newtonian fluids to be investigated include Maxwell and Oldroyd B.Our goal in this project is to develop efficient methods, able to achieve the numerical simulation of three-dimensional flow of mixtures of incompressible viscous fluids with several hundreds to thousands of solid particles. Such large scale simulations have the characteristics of a Grand Challenge in Scientific Computing and success will rely on advanced computational methods implemented on powerful parallel computers. With these simulation tools the scientific community will be able to better understand the complicated mechanisms taking place for example in chemical reactors and in fractured oil reservoirs. Among the consequences of these investigations we can expect for example improved manufacturing techniques for rubber materials and pharmaceutical drugs, and also improved efficiency for drilling techniques used in oil Industry.