Numerical Simulation of Complex Incompressible Viscous Flow in Time Varying Geometries: Applications

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Recent progress by the investigators in the simulation of incompressible viscous flow modeled by the Navier-Stokes equations and their visco-elastic and visco-plastic generalizations in two and three dimensions has led to the proposed work in challenging three-dimensional problems. Specifically, the authors intend to study the direct simulation of pressure-driven particulate flow in three dimensional pipes and horizontal drilling wells, the fluid being either Newtonian or non-Newtonian with the number of particles ranging in the thousands. They will also study the direct numerical simulation of blood flow around three-leaflet prosthetic heart valves. These problems require methodological advances such as the numerical treatment of collisions, the motion of non-spherical objects in viscous fluids and the coupling of fictitious domain and Chimera type methods in order to improve the treatment of boundary layers. During the past six years, the investigators of this award have developed a methodology well suited to numerical simulation of flow in regions with moving boundaries. The resulting methodology has been successfully applied by the authors and other scientists and engineers to the solution of difficult problems from Sciences and Engineering. Among these problems are the direct simulation of sedimentation, fluidization and particle transport phenomena, which play an important role in various areas in Sciences and Engineering (Petroleum Engineering, Food Industry,...). The main goals of this project are to (1) improve the existing methodology so that it can address fluid/particle interaction for particles of relatively complicated shape, (2) develop realistic models and efficient methods for the computational treatment of the collisions taking place in fluid/particle interactions, (3) apply the resulting methodology to an important problem in cardio-vascular medicine namely, the simulation of blood flow/heart valve interaction and (4) simulate slurry transportation in horizontal pipelines and wells, an important issue in enhanced oil recovery. In the heart valve project, the goal is to use the simulation tool to design artificial heart valves generating much less thrombin (a natural blood thickener causing artery clotting) than the ones currently used, which require the patient to take blood thinning drugs which have in general health damaging side effects. The hope is that with an improved design the need for blood thinners will be substantially reduced if not eliminated. This part of project will be done in collaboration with cardio-vascular specialists (including heart surgeons) in the USA and Europe.