Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session FB: Computational Fluid Dynamics I: General Methodology |
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Chair: M. Yousuff Hussaini, Florida State University Room: Tampa Marriott Waterside Hotel and Marina Grand Salon F |
Monday, November 20, 2006 8:00AM - 8:13AM |
FB.00001: Sparse grid collocation schemes for stochastic convection problems Nicholas Zabaras, Baskar Ganapathysubramanian Stochastic Galerkin methods and Monte Carlo based sampling methods have been used to analyze stochastic convection problems. As the complexity of the problem or the number of random variables involved in describing the input uncertainties increases, these approaches become highly impractical. This is especially true in the context of realistic thermal flow problems, where uncertainties in the topology of the boundary domain, boundary flux conditions and heterogeneous physical properties usually require high dimensional random descriptors. The recently proposed Sparse grid Collocation method based on the Smolyak algorithm offers a viable alternate method for solving high dimensional stochastic partial differential equations. An extension of the collocation approach to include adaptive refinement in important dimensions is proposed. We show case the collocation based approach to efficiently solve natural convection problems involving large stochastic dimensions. Equilibrium jumps occurring due to surface roughness and heterogeneous porosity are captured. Comparison of the present method with the GPCE and Monte-Carlo methods are made. [Preview Abstract] |
Monday, November 20, 2006 8:13AM - 8:26AM |
FB.00002: Simulation of a Three-Dimensional Backward-Facing Step Flow Using Entropic LBM and LES Mihail Spasov, Paritosh Mokhasi, Dietmar Rempfer The lattice Boltzmann method (LBM) is considered an attractive alternative to conventional CFD methodologies for the numerical simulation of turbulence in complex geometries because it recovers the Navier-Stokes equations and is computationally efficient and easily parallelizable. Additionally, LBM solves a single continuous particle distribution (which is analogous to the particle distribution function in kinetic theory) on a lattice. The macroscopic properties of the flow field are obtained from these microscopic particle distributions through simple arithmetic integration. Because the macroscopic properties are not solved directly, the LBM avoids solving the Poisson equation for pressure. However the traditional LBMs are only conditionally stable. Entropic lattice Boltzmann methods achieve non-linear stability by adding an analog to the Boltzmann H-theorem to the model. In spite of this non-linear stability entropic LBMs become inaccurate when the flow scales are smaller than the grid size. The use of LES is proposed to avoid this problem. In this talk the use of entropic LBM is presented in conjunction with LES for the particular example of a simulation of the three-dimensional flow over a backward-facing step. The methodology of entropic LBM is discussed as well as the boundary conditions used for the solid walls and the outlet. The results are compared with experimental data and simulations done using other numerical techniques. [Preview Abstract] |
Monday, November 20, 2006 8:26AM - 8:39AM |
FB.00003: Using Graphics Processors for Scientific Computing Blair Perot, Jayson Gadebusch We demonstrate how a low cost ($<$ 100) commodity graphics processor can be used as a vector math co-processor in a conventional PC to increase the speed of scientific calculations by a factor of 3 to 10 times. Direct performance comparisons are made for dot products, sparse matrix vector multiply, and Poisson equation solution via conjugate gradients. A CFD code using the GPU as the primary processor is also demonstrated. The ultimate impact of this technology on high performance scientific computing is discussed. [Preview Abstract] |
Monday, November 20, 2006 8:39AM - 8:52AM |
FB.00004: Unstructured Cartesian/Immersed Boundary Method for Flow Simulations in Complex 3D Geometries Diane de Zelicourt, Chang Wang, Hiroumi Kitajima, Kerem Pekkan, Fotis Sotiropoulos, Ajit Yoganathan Unstructured grids with finite-difference solvers allow one to tackle the complexity of the geometries encountered in numerous engineering or bioengineering applications. However, these are cumbersome to implement and considerably more expensive than similar methods applied on Cartesian grids. In Cartesian methods the arbitrary geometrical complexity can be handled using immersed-interface type algorithms in conjunction with sharp-interface, reconstruction techniques. A major issue is that often the majority of the grid nodes of the background Cartesian mesh within which the flow domain is immersed end up lying outside the computational domain, increasing the memory and computational overhead without increasing the simulation accuracy. The method presented here overcomes this situation by combining the simplicity of the Cartesian grids with the versatility of unstructured grids. We will both demonstrate the efficacy of our methodology and its accuracy by applying it to realistic cardiovascular geometries in the context of the total cavo-pulmonary connection and comparing our results to their experimental counterpart. [Preview Abstract] |
Monday, November 20, 2006 8:52AM - 9:05AM |
FB.00005: A New Formulation of Brinkman Penalization Method for Compressible Flow Simulations in Complex Geometries Qianlong Liu, Oleg V. Vasilyev To simulate flows around solid obstacles of complex geometries, the volume penalization technique, called Brinkman penalization method, was proposed by Arquis and Caltagirone for incompressible viscous flows. Its main idea is to treat solid obstacles as porous media with porosity and permeability approaching zero. This is achieved by adding the penalization terms to the momentum equations. The straightforward extension of the method to compressible viscous flow is to penalize the momentum and energy equations. However, this extension produces unsatisfactory results, mostly due to unphysical wave transmissions into obstacles resulting in considerable energy and mass losses in reflected waves. In this talk, a new formulation of Brinkman penalization method for compressible flows is proposed. In addition to the penalized momentum and energy equations, the continuity equation for the porous media is considered inside obstacles. A sudden change in cross sectional area between fluid and modeled porous media generates a very large acoustic impedance ratio, resulting in ignorable wave transmissions. The new approach is applied to a number of one- and two-dimensional benchmark problems. The direct numerical simulation results for the full compressible high Reynolds viscous flows are in very good agreement with the exact solutions of the inviscid flows. [Preview Abstract] |
Monday, November 20, 2006 9:05AM - 9:18AM |
FB.00006: Runge-Kutta-Chebyshev Projection Method Zheming Zheng, Linda Petzold In this work a fully explicit, stabilized projection method called the Runge-Kutta-Chebyshev (RKC) Projection method is presented for the solution of incompressible Navier-Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step. An additional projection on the time derivative of the velocity is performed whenever a second order approximation for the pressure is desired. We demonstrate both by numerical experiments and by order analysis that the method is second order accurate in time for both the velocity and the pressure. Being explicit, the RKC Projection method is easy to implement and to parallelize. Hence it is an attractive candidate for the solution of large-scale, moderately stiff, diffusion-like problems. [Preview Abstract] |
Monday, November 20, 2006 9:18AM - 9:31AM |
FB.00007: On Further Enhancement of CFD Predictive Algorithms Based on Evidence Theory Svetlana Poroseva, M. Yousuff Hussaini The Dempster-Shafer theory of evidence provides two basic tools -- i) belief functions that represent the degree of belief (confidence) in a given proposition on the basis of given evidence, and ii) Dempster's rule for combining the belief functions generated by different sources in relation to the same proposition. Previously, we have shown that these tools can be used effectively in application to various CFD problems (subsonic flow around the RAE 2822 airfoil and hurricane/typhoon track forecasts). The current study focuses on further enhancement of the predictive algorithms employing Dempster's rule. Specifically, we analyze one of the requirements of Dempster's rule that belief functions corresponding to different sources should be constructed using independent evidence. In CFD problems, evidence is experimental/observational data, which can be quite limited in number and barely sufficient to construct a single belief function. Application of Dempster's rule requires a minimum of two belief functions. We examine the origin of the requirement that independent data be used to construct belief functions and consider a strategy to overcome this constraint and its implications. [Preview Abstract] |
Monday, November 20, 2006 9:31AM - 9:44AM |
FB.00008: A finite-difference formulation for incompressible viscous flow with adaptive mesh refinements Patrick Rabenold, Elias Balaras We propose an adaptive mesh refinement (AMR) strategy, where the computational grid is dynamically refined and derefined in local regions of the computational domain as determined by the local nature and requirements of the flow. In our AMR approach a single-block Cartesian grid solver is employed on a hierarchy of sub-grids with varying spatial resolution. Each of these sub-grid blocks has a structured Cartesian topology, and is part of a tree data structure that covers the entire computational domain. The tree data-structure is implemented using the Paramesh toolkit. We use an explicit second-order projection method on a staggered grid, and the resulting Poisson equation is solved with an iterative multigrid solver. Boundary conditions at the interior boundaries of the sub-grid blocks are enforced using layers of ghost cells which are filled using the solution data from neighboring sub-grid blocks. We will present results that demonstrate that the solver is second order accurate both space and time. Computations of several standard test problems are also in excellent agreement with results in the literature. [Preview Abstract] |
Monday, November 20, 2006 9:44AM - 9:57AM |
FB.00009: Numerical issues in the simulation of variable-density flows Lee Shunn, Frank Ham, Parviz Moin The interaction of variable-density flow-solvers and tabulated state-relationships is explored in the context of combustion and mixing problems. Numerical issues arising from the inconsistent evaluation of density in hydrodynamic simulations are highlighted and discussed. Particular attention is given to the strong coupling that occurs between density, velocity, and pressure in low-Mach number, incompressible flow-solvers. The implications for turbulence and combustion models resulting from numerical complications surrounding this coupling are briefly outlined. An adaptive method that utilizes optimized quadrature-rules over tetrahedral volumes to reliably enforce the equation-of-state in variable-density simulations is developed. The new method is shown to mitigate many of the undesirable artifacts previously observed. A summary of the costs and benefits associated with the adaptive method is given. The method is applied to the large-eddy simulation of a three-dimensional buoyant helium plume, and the simulation results are compared with experimental data and previous computations. [Preview Abstract] |
Monday, November 20, 2006 9:57AM - 10:10AM |
FB.00010: The breakup of a round liquid jet by a coaxial flow of gas using the Refined Level Set Grid Method Dokyun Kim, Marcus Herrmann, Parviz Moin Numerical simulations are conducted to investigate the break-up and atomization of a round liquid jet surrounded by a coaxial flow of gas. A Refined Level Set Grid (RLSG) method coupled to a Lagrangian spray model is used to capture the whole breakup process of the liquid jet. In the near field of the liquid jet, where the primary breakup occurs, motion and topological changes of the liquid jet are described by the RLSG method. In this region, a liquid jet consists of the core and ligaments, which subsequently break into various sizes of drops. The drops generated by the primary breakup are transferred to a Lagrangian stochastic spray model in order to describe the secondary breakup process. The characteristics of the primary breakup in the near-field and statistical properties of the resulting spray are examined for different subgrid scale RLSG primary breakup models. These numerical results demonstrate the applicability and feasibility of our method for simulation of the atomization process of liquid jets in turbulent flows. [Preview Abstract] |
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