Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session AR: CFD: Immersed Boundary and Computational Methods |
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Chair: Sheng Xu, Southern Methodist University Room: 203A |
Sunday, November 23, 2008 8:00AM - 8:13AM |
AR.00001: An Incremental Improvement to the Feedback-Forcing Immersed Boundary Method John Cimbala, Jason DeGraw The immersed boundary method (IBM) has been applied in a variety of forms, but all of them represent a boundary implicitly on a grid that need not conform to the boundary contour. We confine our interest to one of the simpler forms of IBM, the feedback-forcing approach, and apply it via user-defined functions in the commercial cell-centered finite-volume CFD code, FLUENT. The only modification that we make is the addition of a forcing term $\vec{f}= C_{\rm IBM}\left(\vec{v}-\vec{u}\right)$, where $C_{\rm IBM}$ is a problem-dependent penalty parameter, $\vec{v}$ is the velocity of the immersed boundary, and $\vec{u}$ is the fluid velocity. For cells completely contained inside the boundary, we use the forcing term as-is. Cells that are only partially contained inside the boundary are more difficult to treat. In this situation, one approach that has been successfully applied in the literature is to scale the forcing by the fraction of cell volume contained within the boundary. We investigate a modification that scales the forcing in the coordinate directions separately. To test the concept, we applied this modification to two-dimensional flow over a circular cylinder. We found that this approach allows access to higher values of penalty parameter, which typically improves the solution. Tests with other flows are underway at the time of this writing. [Preview Abstract] |
Sunday, November 23, 2008 8:13AM - 8:26AM |
AR.00002: A low-numerical dissipation immersed interface method for the compressible Navier-Stokes equations Carlos Pantano, Kostas Karagiozis, Ramji Kamakoti Immersed interface methods are an alternative methodology to unstructured methods for solving fluid dynamical problems around complex geometries. In this approach, a Cartesian mesh is used to discretize the governing equations and a regular numerical method is used everywhere in the domain, except around the complex boundaries, where special stencils are used. We present and discuss results using a stable numerical methodology for the compressible Navier-Stokes equations that uses centered stencils. Specially designed stencils are constructed around the complex objects to ensure stability. These non-dissipative methods are beneficial in the study of noise and turbulence where numerical dissipation tends to attenuate the relevant flow physics. Furthermore, it is shown that the stiffness introduced by the high-order derivatives of the viscous and heat conduction terms in the discretized equations due to non-deforming boundaries can be resolved into an explicit method. Examples of compressible flows with multiple complex objects at different Mach numbers and Reynolds numbers are presented and convergence of the solutions is investigated as a function of resolution and relative position of the objects with respect to the Cartesian mesh. [Preview Abstract] |
Sunday, November 23, 2008 8:26AM - 8:39AM |
AR.00003: Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles Seokkoo Kang, Iman Borazjani, Fotis Sotiropoulos Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures. [Preview Abstract] |
Sunday, November 23, 2008 8:39AM - 8:52AM |
AR.00004: The Immersed Interface Method for Insect Flight Simulation Sheng Xu The effect of a fluid-solid interface can be represented as a singular force in the Navier-Stokes equations. Two problems arise from this representation. One is how to calculate the force density, and the other is how to treat the force singularity. In the immersed interface method, the latter is solved with second-order accuracy and the sharp fluid-solid interface by incorporating singularity-induced flow jump conditions into discretization schemes. This talk focues on the former problem. In particular, I will present approaches to calculating the force density for both flexible and rigid solids. Results from insect flight simulation will be shown to demonstrate the approaches. [Preview Abstract] |
Sunday, November 23, 2008 8:52AM - 9:05AM |
AR.00005: Efficient Unstructured Cartesian/Immersed-Boundary Method with Local Mesh Refinement to Simulate Flows in Complex 3D Geometries Diane de Zelicourt, Liang Ge, Fotis Sotiropoulos, Ajit Yoganathan Image-guided computational fluid dynamics has recently gained attention as a tool for predicting the outcome of different surgical scenarios. Cartesian Immersed-Boundary methods constitute an attractive option to tackle the complexity of real-life anatomies. However, when such methods are applied to the branching, multi-vessel configurations typically encountered in cardiovascular anatomies the majority of the grid nodes of the background Cartesian mesh end up lying outside the computational domain, increasing the memory and computational overhead without enhancing the numerical resolution in the region of interest. To remedy this situation, the method presented here superimposes local mesh refinement onto an unstructured Cartesian grid formulation. A baseline unstructured Cartesian mesh is generated by eliminating all nodes that reside in the exterior of the flow domain from the grid structure, and is locally refined in the vicinity of the immersed-boundary. The potential of the method is demonstrated by carrying out systematic mesh refinement studies for internal flow problems ranging in complexity from a 90 deg pipe bend to an actual, patient-specific anatomy reconstructed from magnetic resonance. [Preview Abstract] |
Sunday, November 23, 2008 9:05AM - 9:18AM |
AR.00006: ABSTRACT WITHDRAWN |
Sunday, November 23, 2008 9:18AM - 9:31AM |
AR.00007: Domain Decomposition Methods for Solving Stokes-Darcy Systems Based on Boundary Integrals Svetlana Tlupova We consider a coupled problem of Stokes and Darcy equations. This involves solving PDEs of different orders simultaneously. To overcome this difficulty, we apply a non-overlapping domain decomposition method based on a Robin boundary condition obtained by combining the velocity and pressure interface conditions. The coupled system is then reduced to solving each problem separately by an iterative procedure using a Krylov subspace method. The numerical solution in each subdomain is based on the boundary integral formulation, where the kernels are regularized and the leading term in the regularization error is eliminated for higher order accuracy. [Preview Abstract] |
Sunday, November 23, 2008 9:31AM - 9:44AM |
AR.00008: Unstructured Grid Generation via Bubble Packing Method Lilong Wu, Bin Chen Unstructured grid is necessary to numerically simulate the fluid flow in complicated domain. In order to improve the accuracy and efficiency of numerical simulation, a modified physically-based Bubble Packing Method to generate unstructured grid is proposed. In this method the local grid refinement is achieved by adding arbitrary size Bubbles to the real vertices and artificial vertices of the domain. And Shepard interpolation method is used to transfer information from vortices to the inner nodes of the domain, so the mesh density of region can be simply controlled, through which the quality of grid can be improved greatly. At the same time, for the case of curve boundary, the process of initial Bubble and dynamic relaxation is realized by mapping the curve to a straight line and the parameterization of arc-length, which ensures that all edge Bubbles move only on their associated curve. Moreover, the improved BPM is applied to generate unstructured grid with local refinement near the boundary of square domain to simulate the lid-driven flow in a square cavity with Re=1000. The good agreement between numerical result and the benchmark verifies the grid quality and the validation of numerical algorithm on the unstructured grid. [Preview Abstract] |
Sunday, November 23, 2008 9:44AM - 9:57AM |
AR.00009: Fluid Velocity Superposition method for fluid-structure interaction in viscous flows using the Immersed Boundary Method Alex Szatmary, Charles Eggleton The Immersed Boundary Method conventionally uses Chorin's spectral projection method as a viscous flow solver due to its computational speed and high degree of convergence. These advantages hold most fully for Fourier basis functions (which suppose periodic boundary conditions). It is advantageous to extend the capabilities of the spectral projection method to viscous flow with non-periodic boundary conditions. Here, a technique is proposed in which fluid velocity is represented as the superposition of a non-periodic mean velocity profile and a periodic disturbance due to the presence of an immersed body. The spectral projection method is then applied only to the disturbance velocity. The proposed method is tested by simulating the deformation of a capsule in unbounded linear flow fields with both extensional and shear components, as well as in shear flows near a wall. Accuracy of these results is confirmed by comparison with theory in the limit of small deformations and numerical results for finite deformation from the literature. [Preview Abstract] |
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