Browsing by Subject "Immersed Boundary Method"
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Item Convergence analysis of the immersed boundary method.(2011-12) Liu, YangMany problems involving internal interfaces can be formulated as partial differential equations with singular source terms. Numerical approximation to such problems on a regular grid necessitates suitable regularizations of delta functions. We study the convergence properties of such discretizations for constant coefficient elliptic problems using the Immersed Boundary (IB) method, which is both a mathematical formulation and a numerical scheme widely used to solve fluid-structure interaction problems, as an example. IB schemes use a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh for the immersed structure, and discrete delta functions for communication between these two grids. We show how the order of the differential operator, order of the finite difference discretization, and properties of the discrete delta function all influence the local convergence behavior. In particular, we show how a recently introduced property of discrete delta functions - the smoothing order - is important in the determination of local convergence rates. We apply our theories to stationary Stokes flow problem and obtain both local and L^P convergence results. We examine the predicted results with numerical simulations.Item Fluid-Structure Interaction Simulation of Complex Floating Structures and Waves(2015-11) Calderer Elias, AntoniA novel computational framework for simulating the coupled interaction of complex floating structures with large-scale ocean waves and atmospheric turbulent winds has been developed. This framework is based on a domain decomposition approach coupling a large-scale far-field domain, where realistic wind and wave conditions representative from offshore environments are developed, with a near-field domain, where wind-wave-body interactions can be investigated. The method applied in the near-field domain is based on a partitioned fluid-structure interaction (FSI) approach combining a sharp interface curvilinear immersed boundary (CURVIB) method with a two-phase flow level set formulation and is capable of solving free surface flows interacting non-linearly with complex real life floating structures. An aspect that was found critical in FSI applications when coupling the structural domain with the two-fluid domain is the approach used to calculate the force that the fluid exerts to the body. A new force calculation approach, based on projecting the pressure on the surface of the body using the momentum equation along the local normal to the body direction, was proposed. The new approach was shown, through extensive numerical tests, to greatly improve the ability of the method to correctly predict the dynamics of the floating structure motion. For the far-field domain, a large-scale wave and wind model based on the two-fluid approach of Yang and Shen (JCP 2011), which integrates a viscous Navier-Stokes solver with undulatory boundaries for the motion of the air and an efficient potential-flow based wave solver, was employed. For coupling the far-field and near-field domains, a wave generation method for incorporating complex wave fields into Navier-Stokes solvers has been proposed. The wave generation method was validated for a variety of wave cases including a broadband spectrum. The computational framework has been further validated for wave-body interactions by replicating an experiment of floating wind turbine model subject to different sinusoidal wave forces. The simulation results, which agree well with the experimental data, have been compared with other numerical results computed with available numerical codes based on lower order assumptions. Despite the higher computational cost of our method, it yields to results that are in overall better accuracy and it can capture many additional flow features neglected by lower order models. Finally, the full capabilities of the framework have been demonstrated by carrying out large eddy simulation (LES) of a floating wind turbine interacting with realistic ocean wind and wave conditions.Item Numerical Simulation Of The Atmospheric Boundary Layer Over Complex Topography: A Modern Approach To A Classical Problem(2020-05) Andersen, NoahNumerical methods were developed and validated to simulate the atmospheric boundary layer (ABL) using large eddy simulation (LES). This framework captures the topography of the Earth’s surface rather than modeling it. To robustly simulate the ABL, four unique capabilities (temperature transport, topographic data, immersed boundary method with wall modeling, and turbulent inflow generation) were added to a traditional finite difference computational fluid dynamics code. The accuracy of each capability was analyzed individually using validation tests. Then, a full scale simulation of the ABL over a tidal inlet was conducted. It was found that the resolved topography of the Earth’s surface had a significant effect on the flow field. Furthermore, it was found that the results from LES are more accurate than mesoscale simulations. Lastly, it was found that the errors in the present simulation are a result of the roughness model used over the sea surface.