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The thesis presents a fluid-structure interaction studies on the hemodynamics of blood flow in the left ventricle and through the mitral valve. The virtual model consists of a mathematical model of the left ventricle coupled with a complex and structurally flexible bi-leaflet valve representing the mitral opening. The mitral valve is a bicuspid valve with anterior and posterior leaflets and it regulates unidirectional blood flow from the left atrium to the left ventricle in the diastole phase. The leaflets are made of chordae, annulus and papillary muscles. The goal of this study is to provide biomedical engineers and clinical physicians with a virtual laboratory tool to understand the dynamics of blood flow in a diseased heart and aid in the design of novel artificial heart valves. To this end, the simulation studies present an increasingly complex model of the heart to evaluate the vortex ring formation and evolution of the diastole phase in the left ventricle; and to characterize the septal-anterior motion in a diseased heart with obstructive hypertrophic cardiomyopathy. Finally, in collaboration with an industrial partner, the fluid-structure modeling framework was used to evaluate the performance of a new accelerated artificial valve tester. / Graduate

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Computational fluid dynamics (CFD) plays an important role in many scientific applications, ranging from designing more effective boat engines or aircraft wings to predicting tomorrow's weather, but at the cost of requiring huge amounts of computing time. Also, traditional algorithms suffer from scalability limitations, making them hard to parallelize massively. As a relatively new and promising method for computational fluid dynamics, the Lattice Boltzmann algorithm tries to solve the scalability problems of conventional, but well-tested algorithms in computational fluid dynamics. Through its inherently local structure, it is well suited for parallel processing, and has been implemented on many different kinds of parallel platforms. Adapteva's Epiphany platform is a modern, low-power manycore architecture, which is designed to scale up to thousands of cores, and has even more ambitious plans for the future. Hardware support for floating-point calculations makes it a possible choice in scientific settings. The goal of this thesis is to analyze the performance of the Lattice Boltzmann algorithm on the Epiphany platform. This is done by implementing and testing the lid cavity test case in two and three dimensions. In real applications, high performance on large lattices with millions of nodes is very important. Although the tested Epiphany implementation scales very good, the hardware does not provide adequate amounts of local memory and external memory bandwidth, currently preventing widespread use in computational fluid dynamics.

Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

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No description available.

Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached. A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity. Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.