Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session AL: CFD I: Methods |
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Chair: Elias Balaras, University of Maryland Room: 200A |
Sunday, November 22, 2009 8:00AM - 8:13AM |
AL.00001: A divergence preserving Adaptive Mesh Refinement strategy for viscous incompressible flows M. Vanella, E. Balaras Structured adaptive mesh refinement (S-AMR) concentrates computational resources (i.e. grid points) in high-gradient regions of the flow, while maintaining most of the desirable properties of structured Cartesian solvers. Whenever the computational grid is locally refined/derefined the flow variables in S-AMR calculations need to maintain certain conservation properties during restriction or prolongation operations. Restriction refers to the transfer of a flow variable from a grid at a fine level of refinement to an underlying grid at a coarser level, while prolongation is the data transfer in the inverse direction. Of particular interest in S- AMR applications in viscous incompressible flows are divergence-preserving prolongation operators of a vector field. When the mesh refinement-derefinement procedure is applied after the predictor step of the fractional step integration scheme, divergence preservation for prolongation is crucial to avoid spurious pressure oscillations and additional errors on the computed flow field. In this work we propose method for divergence-preserving prolongation applicable to nested grids that differ by a factor of two in terms of resolution. The accuracy of the method is evaluated on prototypical laminar flows, like the Taylor-Green vortex problem and flow around a cylinder. [Preview Abstract] |
Sunday, November 22, 2009 8:13AM - 8:26AM |
AL.00002: Towards a Fully Adaptive Mesh-Free Method for Solving Viscous Incompressible Flows Paritosh Mokhasi, Dietmar Rempfer A fully adaptive mesh-free method based on radial basis functions (RBF) is proposed for numerically solving the Navier- Stokes equations. The scheme is based on the method of lines wherein the spatial derivatives are approximated using a differential quadrature approach. The solution is progressed in time using a fractional step method with pressure correction. To demonstrate its flexibility, the 2D driven cavity problem is solved in the Eulerian and semi-Lagrangian framework using radial basis functions. We further demonstrate, via a 1D spatio- temporal example, that using RBFs adaptively enables one to produce highly accurate results. Finally, we present algorithms for solving a large class of fluid dynamics problems using radial basis functions. [Preview Abstract] |
Sunday, November 22, 2009 8:26AM - 8:39AM |
AL.00003: A spectral multidomain penalty method model for high Reynolds number incompressible flows Jorge Escobar-Vargas, Peter Diamessis We present our latest results towards the development of a spectral multidomain penalty method-based incompressible Navier-Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains. Temporal discretization of the governing equations is based on three fractional steps (explicit advancement of nonlinear terms and implicit treatment of pressure and viscous terms). The spatial discretization uses a Legendre collocation approach in discontinuous quadrilateral subdomains. Numerical stability is enabled through a penalty scheme, spectral filtering and appropriately defined dealiasing. The conditioning of the linear system associated with the discretized Poisson equation for the pressure is analyzed in detail. In addition, the efficiency of various preconditioning strategies such as diagonal and block Jacobi, finite difference, and additive Schwartz are investigated. Finally, the efficiency and accuracy of the Navier Stokes solver are assessed through application to select test cases. [Preview Abstract] |
Sunday, November 22, 2009 8:39AM - 8:52AM |
AL.00004: Wavelet regularization of the 2D incompressible Euler equations Romain Nguyen van Yen, Marie Farge, Kai Schneider We examine the viscosity dependence of the solutions of two-dimensional Navier-Stokes equations in periodic and wall-bounded domains, for Reynolds numbers varying from $10^3$ to $10^7$. We compare the Navier-Stokes solutions to those of the regularized two-dimensional Euler equations. The regularization is performed by applying at each time step the wavelet-based CVS filter {\it (Farge et al., Phys. Fluids, 11, 1999)}, which splits turbulent fluctuations into coherent and incoherent contributions. We find that for Reynolds $10^5$ the dissipation of coherent enstrophy tends to become independent of Reynolds, while the dissipation of total enstrophy decays to zero logarithmically with Reynolds. In the wall-bounded case, we observe an additional production of enstrophy at the wall. As a result, coherent enstrophy diverges when Reynolds tends to infinity, but its time derivative seems to remain bounded independently of Reynolds. This indicates that a balance may have been established between coherent enstrophy dissipation and coherent enstrophy production at the wall. The Reynolds number for which the dissipation of coherent enstrophy becomes independent on the Reynolds number is proposed to define the onset of the fully-turbulent regime. [Preview Abstract] |
Sunday, November 22, 2009 8:52AM - 9:05AM |
AL.00005: A Multigrid Accelerated High-Order Compact Fractional Step Method for Unsteady Incompressible Viscous Flows Omer San, Anne Staples An efficient high-order compact scheme is presented for computing unsteady incompressible viscous flows. The scheme is constructed on a staggered Cartesian grid. Using the fractional step framework, the Navier-Stokes equations are advanced in time with the second-order Adams-Bashforth method without considering the pressure terms in the predictor step. The velocity field is then corrected so that the continuity equation is satisfied through a pressure Poisson equation. Since the efficiency of the fractional step method depends on the Poisson solver, a Mehrstellen-based V-cycle multigrid acceleration is implemented in the solution of the Poisson equation to enhance the computational efficiency. The method is validated by simulating a decaying Taylor-Green vortex. The results show that the method has high resolving efficiency, drastically reduced computational time, and high-order accuracy, making it applicable for the simulation of complex turbulent flows. [Preview Abstract] |
Sunday, November 22, 2009 9:05AM - 9:18AM |
AL.00006: Vortex-induced vibrations of a long flexible cylinder in transitional and turbulent flows Remi Bourguet, George Karniadakis, Michael Triantafyllou The flow past a flexible cylinder subject to Vortex-Induced Vibrations (VIV) is investigated by direct numerical simulation at low and moderate Reynolds numbers (Re$=100-1000$). The cylinder of large spanwise extension ($\ge 200$ diameters) is pinned and hinged at both ends and its central part is free to move in all directions under the effect of fluid-structure interaction. The cylinder dynamic is governed by a beam-cable equation. The influence of Reynolds number and structural parameters such as tension, bending stiffness and mass ratio, on VIV amplitudes and characteristic frequencies is quantified. The relationship between hydrodynamic efforts, structure motion and vortex shedding pattern is examined during the transition to turbulence. In particular, modifications of the alternating shedding pattern related with specific VIV conditions are analyzed in respect to the appearance of space/time irregularities in the structure response. [Preview Abstract] |
Sunday, November 22, 2009 9:18AM - 9:31AM |
AL.00007: A novel computational method to determine the dynamics of a lipid bilayer vesicle in a viscous flow David Salac, Michael Miksis Models of lipid bilayer vesicle motion require that both the local area element of the interface and the volume enclosed by the interface be conserved. Here we present a novel level-set computational method to predict the dynamics of a vesicle under the influence of an external viscous fluid. The fluid both inside and outside the vesicle is governed by the Navier-Stokes equations. We impose both the volume and area constraint by implementing a novel splitting scheme. Similar to standard pressure-correction methods for the Navier-Stokes equations, which require the velocity field to be divergence free, we solve a variable coefficient pressure-Poisson equation with Neumann boundary conditions to ensure volume conservation. We also impose the constraint that the velocity field must be divergence free on the moving interface. This necessitates the solution of an additional partial differential equation. This equation and the needed boundary conditions will be presented. Numerical examples of the scheme and convergence checks will also be presented. [Preview Abstract] |
Sunday, November 22, 2009 9:31AM - 9:44AM |
AL.00008: Two layer fluid stress analysis during airway closure Cheng-Feng Tai, David Halpern, James Grotberg The airways are lined with a film consisting of two immiscible liquids, a serous layer and a more viscous mucus layer. Due to a surface tension driven instability, a liquid plug can form that obstructs the passage of air along the airways provided the ratio of the film thickness to the tube radius is greater than a critical value $\sim $0.12. In this study, we assume that the liquid layers are Newtonian, the surface tension is constant at the interfaces and the air-core phase is passive. We solve the Navier-Stokes and continuity equations subject to interfacial stress conditions and kinematic boundary conditions numerically using a finite volume approach in conjunction with a sharp interface method for the interfaces. Surface tension, viscosity and film thickness ratios can be altered by disease, and their influence on the closure instability is investigated. Results show that the shear and normal stresses along the airway walls can be strong enough to injure airway epithelial cells. We acknowledge support from the National Institutes of Health grant number NIH HL85156. [Preview Abstract] |
Sunday, November 22, 2009 9:44AM - 9:57AM |
AL.00009: Feasibility of using Hybrid Wavelet Collocation - Brinkman Penalization Method for Shape and Topology Optimization Oleg V. Vasilyev, Mattia Gazzola, Petros Koumoutsakos In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape and topology optimization of fluid flows. Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid in complex geometries (where grid resolution varies both in space and time time), while Brinkman volume penalization allows easy variation of flow geometry without using body-fitted meshes by simply changing the shape of the penalization region. The use of Brinkman volume penalization approach allow seamless transition from shape to topology optimization by combining it with level set approach and increasing the size of the optimization space. The approach is demonstrated for shape optimization of a variety of fluid flows by optimizing single cost function (time averaged Drag coefficient) using covariance matrix adaptation (CMA) evolutionary algorithm. [Preview Abstract] |
Sunday, November 22, 2009 9:57AM - 10:10AM |
AL.00010: Uncertain shape optimization for dense gas flows Pietro Marco Congedo, Christophe Corre, Jean-Marc Martinez Uncertain shape optimization is a fascinating but challenging task. Our work explores some key issues in uncertain optimization and proposes a strategy to obtain a more reliable solution at a moderate computational cost. The steady transonic inviscid flow of a dense gas over an airfoil is considered and a shape optimization performed to minimize the airfoil's drag coefficient. Three sources of uncertainties are accounted for : thermodynamic model, freestream conditions and geometry. The combined effect of these uncertainties is analyzed to get the average and variance of the drag coefficient, that are both minimized during the optimization. Preliminary stochastic simulations based on polynomial chaos expansions yield the most influent uncertain parameters; several optimization strategies are then studied, with an original combination of response surfaces and metamodels, to obtain robust optimal solutions for a limited number of flow computations. [Preview Abstract] |
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