Browsing by Author "Behr, Marek"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Computational hemodynamics: Hemolysis and viscoelasticity(2006) Arora, Dhruv; Behr, Marek; Pasquali, MatteoComputational Fluids Dynamics (CFD) has emerged as a viable and reliable design tool for the analysis of blood-handling devices. The CFD-based design is simple, time- and cost-effective; the method predicts accurately the hydraulic performance of these devices. However, the CFD-based hematologic design is in its infancy. This thesis presents a holistic design approach for centrifugal blood pumps. The flow through the pump is simulated with a novel finite element method that accounts efficiently for deformable domains and moving parts while retaining desirable scalability on distributed-memory computers. The method is validated successfully against literature results in a benchmark problem of flow past a stirrer in a square cavity. Blood is treated as a Newtonian fluid in these initial simulations. However, blood is known to display shear-thinning and viscoelasticity; a generalized Newtonian model is employed to capture the shear-thinning blood viscosity, and the flow through the GYRO pump (Baylor College of Medicine) is simulated in typical operating conditions. The overall hydraulic performance predicted by the shear-thinning model show little difference compared to the Newtonian results. However, the shear-thinning model predicts smaller recirculation regions and higher values of wall shear stress. For simulating viscoelasticity, a new family of three-field Galerkin/Least-Squares stabilized finite element methods is constructed and evaluated in the benchmark flow past a cylinder placed in a channel. The results are compared with the state-of-the-art numerical results and good agreement is found for the drag predictions. Mesh convergence is demonstrated for the new methods. Finally, a new tensor-based blood-damage model is proposed; the model is based on the analogy between red blood cells and fluid droplets. The model is compared with the traditional method of hemolysis prediction in homogeneous steady and unsteady flows and inhomogeneous time-dependent flow in two-dimensional and three-dimensional blood pump. The predictions of hemolysis by the tensor-based method are found to agree well with flow-loop experimental results on bovine blood in the GYRO pump.Item Shape Optimization in Unsteady Blood Flow: A Numerical Study of Non-Newtonian Effects(2004-08) Abraham, Feby; Behr, Marek; Heinkenschloss, MatthiasThis paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two-dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the Carreau-Yasuda model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the Carreau-Yasuda model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.Item Stabilized finite element solution of optimal control problems in computational fluid dynamics(2004) Abraham, Feby V.; Behr, MarekThis thesis discusses the solution of optimal flow control problems, with an emphasis on solving optimal design problems involving blood as the fluid. The discretization of the governing equations of fluid flow is accomplished using stabilized finite element formulations. Although frequently and successfully applied, these methods depend on significant mesh refinement to establish strong consistency properties, when using low-order elements. We present an approach to improve the consistency properties of such methods. We develop the methodology for the numerical solution of optimal control problems using the aforementioned discretization scheme. For two possible approaches in which the optimal control problem can be discretized---optimize-then-discretize and discretize-then-optimize---we use a boundary control problem governed by the linear Oseen equations to numerically explore the influence of stabilization. We also present indicators for assessing the quality of the computed solution. We then investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the Carreau-Yasuda model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. For a steady flow scenario, we apply gradient-based optimization procedure to a benchmark problem of flow through a right-angle cannula, and to a flow through an idealized arterial graft. We present the issues involved in solving large-scale optimal design problems, and state the numerical formulations for the various approaches that could be used to solve such problems. We numerically demonstrate optimal shape design for unsteady flow in an arterial graft.