Simulation of the flow around a submerged structure using the Immersed Boundary Method

Water Qualit

A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries

We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson equation is solved on a level-by-level basis, using a "one-way interface" scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of Computational Physic

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations

Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method

Flight has fascinated humans for centuries. Human inventions such as missiles, aircraft , unmanned aerial vehicles (UAV), and micro air vehicle (MAV) are inspired by natural flying expertise. As natural flyers usually operate in a vortex-dominated environment, interactions between their wings and the vortices have significant influences on force generation and flying efficiency. Some interesting phenomena induced from such vortex-body interactions have gotten a lot of attention in the past few decades. A good example is that birds and insects are credited with extracting energy from ambient vortices. In a simpler form, bio-inspired airfoils with either passive or active flapping motions are found to have the potential to harvest energy from incoming vortices generated from an upstream object, i.e. a cylinder. The current study identified the interaction modes of the leading edge vortex (LEV) and trailing edge vortex (TEV) between the active flapping airfoil and the incoming vortices. The relation between the interaction modes and the energy extraction capacity of an active harvester is investigated guided by a potential theory. The interaction modes induced by a passive energy harvester always benefit the energy extraction efficiency. However, the dynamic response of the passive harvester was found to vary corresponding to the properties of the incoming vortical wake. A profound appreciation of energy extracting mechanisms can provide a solution for the energy consumption issue of MAV and UAV. However, difficulties are encountered in practical applications of energy harvesting on how to detect the locations of generated vortices and what the trajectory of the vortex downstream of the moving body is. Some observations are realized and the fluid dynamics of the phenomena is beyond the fundamentals described in the textbook. One well-known instance is the asymmetric wake formed downstream of a symmetric sinusoidal heaving airfoil. In this study, factors that influence the formation of the asymmetric wakes on both the near wake and far wake regions are demonstrated. Novel vortex models are developed to explore the vortex dynamic mechanisms of the asymmetric wake and its development from the near wake region to the far wake region. In order to analyze the flow fields for the bio-inspired problems, Computational Fluid Dynamics (CFD) provides powerful and convenient tools. The shape of bio-inspired wings/airfoils and their maneuvers are usually very complicated. In CFD, the immersed-boundary (IB) method is an advantageous approach to simulate such problems. In this study, an immersed-boundary method is implemented in a parallel fashion in order to speed up the computational rate.. A variety of numerical schemes have been applied to the IB method, including different spatial schemes and temporal schemes; their performances are investigated. In addition, the IB method has been successfully implemented with the fluid-structure interaction models for studying passive mobile objectives, i.e. the energy harvester. The possibility of coupling other fluid dynamic models, i.e. species transport model and turbulence models, is also demonstrated

Numerical Simulations of the Two-phase flow and Fluid-Structure Interaction Problems with Adaptive Mesh Refinement

Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high grid resolution is usually needed. However, one does not need or maybe cannot afford a fine grid of uniformly high resolution across the whole domain. The need to resolve local fine features can be addressed by the adaptive mesh refinement (AMR) method, which increases the grid resolution in regions of interest as needed during the simulation while leaving general estimates in other regions. In this work, we propose a block-structured adaptive mesh refinement (BSAMR) framework to simulate two-phase flows using the level set (LS) function with both the subcycling and non-subcycling methods on a collocated grid. To the best of our knowledge, this is the first framework that unifies the subcycling and non-subcycling methods to simulate two-phase flows. The use of the collocated grid is also the first among the two-phase BSAMR framework, which significantly simplifies the implementation of multi-level differential operators and interpolation schemes. We design the synchronization operations, including the averaging, refluxing, and synchronization projection, which ensures that the flow field is divergence-free on the multi-level grid. It is shown that the present multi-level scheme can accurately resolve the interfaces of the two-phase flows with gravitational and surface tension effects while having good momentum and energy conservation.Comment: 178 page