Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L5: CFD V: Numerical Methods II |
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Chair: Marcus Hermann, Arizona State University Room: 308 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L5.00001: On the accuracy of difference formulas at block interfaces in Structured Adaptive Mesh Refinement (S-AMR) methods Marcos Vanella, Elias Balaras S-AMR is a cost/efficient strategy to solve a variety of complex problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different resolution levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. This generates coarse-fine interfaces between blocks whose treatment affects the accuracy and conservation properties of solver. In the present study we will focus on the effects of different interpolation strategies on the properties of finite-differences taken at block boundaries or cells neighboring the boundaries. Looking into a set of model problems we found that for a variety of popular interpolation schemes (both low and high order) the symmetry properties of central difference operators are lost and dissipation and phase errors are added to the errors of the difference formulas. Recurring interpolation, in particular, degrades the quality of formulas as more coarse and fine point values are introduced in an asymmetric manner. Solution strategies based on the minimization of the modified wavenumber error will be presented. [Preview Abstract] |
Monday, November 21, 2011 3:48PM - 4:01PM |
L5.00002: A Method of Adaptive Mesh Refinement on Cartesian Unstructured Meshes Carlos Ballesteros, Marcus Herrmann A general method for a dynamic meshing library with built-in localized adaptive mesh refinement (AMR) routines for hexahedral meshes is presented. Current block-based AMR methods apply stacked nested finer grids to regions of the computational domain, solve the governing equations of the flow within the fine grid, and then interpolate the fine grid values to the coarse grid. Unlike existing libraries, the proposed method is designed to generate fully unstructured grids that may be refined and coarsened on-the-fly up to an arbitrary level. This approach allows for \emph{h}-refinement without the memory and computational expense of calculating masked coarse grid cells, as is done in block-based AMR. The hexahedral nature of the meshes simplifies the finite-volume algorithms, reducing the computational expense of refinement when compared with arbitrary tetrahedral-mesh solvers. Complex surfaces can be quickly modeled by successive refinement of control volumes while retaining numerical stability and minimizing the size of the grid. [Preview Abstract] |
Monday, November 21, 2011 4:01PM - 4:14PM |
L5.00003: A fully conservative finite-volume method for incompressible Navier-Stokes equations on locally refined nested Cartesian grids Adamandios Sifounakis, Donghyun You, Satbir Singh A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher- order conservation principles - {\it i.e.}, in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Hanging nodes at the interface are {\it implicitly} slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is found to significantly improve the computational efficiency while it is straightforward to implement. The present method shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids in simulations of Taylor vortex, lid-driven cavity flow, and flow over a square cylinder. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L5.00004: A Space/Time Dynamically Adaptive Method for Multiscale Problems Temistocle Grenga, Zachary Zikoski, Samuel Paolucci, Mauro Valorani Systems of partial differential equations (PDEs) describing problems that are multiscale in space and time are computationally very expensive to solve. In order to overcome the challenges related to both thin spatial layers and temporal stiffness we propose the use of a wavelet adaptive multilevel representation (WAMR) in space and an adaptive model reduction method (G-Scheme) in time. The multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution. High resolution computations are performed only in spatial regions where sharp transitions occur, while the G-Scheme is an explicit solver developed for stiff problems which is built upon a local decomposition of the dynamics in three subspaces involving slow, active and fast time scales. Only the modes in the active subspace are integrated numerically, the others are approximated asymptotically. Subsequently, the original problem not only becomes substantially smaller, but more importantly non-stiff. Combining the WAMR technique with the G-Scheme yields a time accurate solution of a prescribed accuracy with a much smaller number of space- time degrees of freedom. While the computational scheme can be used to solve a wide class of stiff PDE problems, we will illustrate its use in the solution of the Navier Stokes equations in reactive flows. [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L5.00005: Parallel Adaptive Wavelet Collocation Method for PDEs Oleg V. Vasilyev, AliReza Nejadmalayeri, Alexei Vezolainen A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows to perform wavelet transform and derivative calculations on each processor without additional data synchronization on each level of resolution. The data are stored using tree-like structure with tree roots starting at sufficiently large level of resolution to shorten tree traversing path and to minimize the size of trees for data migration. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quantum of data to be migrated between the processors. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during grid adaptation step and reassigning tree data structure nodes to the appropriate processors to ensure approximately the same number of nodes on each processor. The parallel efficiency of the approach is discussed based on parallel Coherent Vortex Simulations of homogenous turbulence with linear forcing at effective non-adaptive resolutions up to $2048^3$ using as many as $1024$ CPU cores. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L5.00006: A Hybrid Grid Compressible Flow Solver for Large-Scale Supersonic Jet Noise Simulations on Multi-GPU Clusters Andrew Corrigan, K. Kailasanath, Junhui Liu, Ravi Ramamurti, Douglas Schwer A compressible flow solver for multi-GPU clusters has been developed for performing large-scale supersonic jet noise and other high-speed compressible flow simulations over hybrid grids. While supersonic jet noise simulations require the accurate representation of complex nozzle geometry and thus the use of unstructured grids, much of the domain geometry can be represented sufficiently with structured grids, which drastically reduces memory bandwidth consumption and storage. Therefore, hybrid grids are employed, which combine an unstructured grid representation in the vicinity of the nozzle with a structured grid representation in the wake region of the flow field. Performance benchmarks are drawn from large-scale runs performed using this solver, including a jet nozzle with chevrons and multi-species flows involving jet engine exhaust. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L5.00007: Numerical study on the onset of electro-convection between planar electrodes caused by unipolar charge injection Dolfred Vijay Fernandes, Suresh Alapati, Yong Kweon Suh Two-dimensional electrohydrodynamic (EHD) convection in a dielectric liquid between a pair of planar electrodes has been studied numerically considering autonomous unipolar charge injection from the bottom electrode. The steep gradient in the charge-density distribution and its time evolution can be resolved successfully using upwind schemes for the convective terms in the charge conservation equation. The Navier-Stokes equations coupled with the charge conservation equation and the Poisson equation for the potential are solved using the SIMPLE algorithm. We also apply a perturbation method to study the linear stability problem to derive more accurate critical parameter values for the onset of electro-convection. In particular, we are interested in the effect of injection strength and the horizontal length of the domain on the stability characteristics. Our two-dimensional numerical solutions are compared with the linear stability analysis for the validation of the code. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L5.00008: Vorticity confinement technique for drag prediction Alex Povitsky, Troy Snyder This work couples wake-integral drag prediction and vorticity confinement technique (VC) for the improved prediction of drag from CFD simulations. Induced drag computations of a thin wing are shown to be more accurate than the more widespread method of surface pressure integration when compared to theoretical lifting-line value. Furthermore, the VC method improves trailing vortex preservation and counteracts the shift from induced drag to numerical entropy drag with increasing distance of Trefftz plane downstream of the wing. Accurate induced drag prediction via the surface integration of pressure barring a sufficiently refined surface grid and increased computation time. Furthermore, the alternative wake-integral technique for drag prediction suffers from numerical dissipation. VC is shown to control the numerical dissipation with very modest computational overhead. The 2-D research code is used to test specific formulations of the VC body force terms and illustrate the computational efficiency of the method compared to a ``brute force'' reduction in spatial step size. For the 3-D wing simulation, ANSYS FLUENT is employed with the VC body force terms added to the solver with user-defined functions (UDFs). VC is successfully implemented to highly unsteady flows typical for Micro Air Vehicles (MAV) producing oscillative drag force either by natural vortex shedding at high angles of attack or by flapping wing motion. [Preview Abstract] |
Monday, November 21, 2011 5:19PM - 5:32PM |
L5.00009: Computational and experimental study of airflow around a fan powered UVGI lamp Srikar Kaligotla, Behtash Tavakoli, Mark Glauser, Goodarz Ahmadi The quality of indoor air environment is very important for improving the health of occupants and reducing personal exposure to hazardous pollutants. An effective way of controlling air quality is by eliminating the airborne bacteria and viruses or by reducing their emissions. Ultraviolet Germicidal Irradiation (UVGI) lamps can effectively reduce these bio-contaminants in an indoor environment, but the efficiency of these systems depends on airflow in and around the device. UVGI lamps would not be as effective in stagnant environments as they would be when the moving air brings the bio-contaminant in their irradiation region. Introducing a fan into the UVGI system would augment the efficiency of the system's kill rate. Airflows in ventilated spaces are quite complex due to the vast range of length and velocity scales. The purpose of this research is to study these complex airflows using CFD techniques and validate computational model with airflow measurements around the device using Particle Image Velocimetry measurements. The experimental results including mean velocities, length scales and RMS values of fluctuating velocities are used in the CFD validation. Comparison of these data at different locations around the device with the CFD model predictions are performed and good agreement was observed. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L5.00010: Integration Techniques for Stokes Boundary Integrals Mike Nicholas Stokes flow is often approached through a boundary integral formulation. The integrals involved are singular or nearly singular and therefore are not resolved well through standard quadrature methods. Various techniques to improve the accuracy of such integrals exist. We will present a brief survey of methods for singular and nearly singular Stokes integrals for both 2D and 3D flows. [Preview Abstract] |
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