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 H5: CFD IV: Numerical Methods I |
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Chair: Anne Staples, Virginia Polytechnic Institute and State University Room: 308 |
Monday, November 21, 2011 10:30AM - 10:43AM |
H5.00001: A Simple and Efficient Parallel Implementation of the Fast Marching Method Jianming Yang, Frederick Stern The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of applications. However, this method is inherently serial and doesn't lend itself to a straightforward parallelization. In this study, we present a simple and efficient algorithm for the parallel implementation of the fast marching method using a domain decomposition approach. Properties of the Eikonal equation are explored to greatly relax the serial interdependence of neighboring sub-domains. Overlapping sub-domains are employed to reduce communication overhead and improve parallelism among sub-domains. There are no iterative procedures or rollback operations involved in the present algorithm and the changes to the serial version of the fast marching method are minimized. Examples are performed to demonstrate the efficiency of our parallel fast marching method. [Preview Abstract] |
Monday, November 21, 2011 10:43AM - 10:56AM |
H5.00002: ABSTRACT WITHDRAWN |
Monday, November 21, 2011 10:56AM - 11:09AM |
H5.00003: A new fully explicit algorithm for incompressible flows Sangro Park, Changhoon Lee The Poisson equation for pressure arising from nonzero divergence of the nonlinear term in the integration of the Navier-Stokes equations requires a lot of computational cost except for cases with periodic domain. In order to mitigate this cost, we propose a new project algorithm which is fully explicit, thus not requiring iterations. The projection operator, $1-\kappa_i \kappa_j / \kappa^2$, which projects any vector field with divergence into the divergence-free subspace in the Fourier space, when transformed into the physical space, shows decaying distribution with the distance from the point in question. This allows truncation so that the resulting local distribution of the projection operator, through convolution, can be used to obtain projected nonlinear terms which has relatively small divergence. This ``approximate'' projection scheme was then applied to direct numerical simulation of isotropic turbulence to investigate effectiveness and efficiency of the scheme in reducing divergence and correct projection of the nonlinear terms through the statistical properties of the turbulent flow. Performance of the scheme in a variety of aspects is investigated and details will be presented in the meeting. [Preview Abstract] |
Monday, November 21, 2011 11:09AM - 11:22AM |
H5.00004: A coarse-grid projection method for accelerating incompressible flow computations Omer San, Anne Staples We present a coarse-grid projection (CGP) algorithm for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. Here, we investigate a particular CGP method for the vorticity-stream function formulation that uses the full weighting operation for mapping from fine to coarse grids, the third-order Runge-Kutta method for time stepping, and finite differences for the spatial discretization. After solving the Poisson equation on a coarsened grid, bilinear interpolation is used to obtain the fine data for consequent time stepping on the full grid. We compute several benchmark flows: the Taylor-Green vortex, a vortex pair merging, a double shear layer, decaying turbulence and the Taylor-Green vortex on a distorted grid. In all cases we use either FFT-based or V-cycle multigrid linear-cost Poisson solvers. Reducing the number of degrees of freedom of the Poisson solver by powers of two accelerates these computations while, for the first level of coarsening, retaining the same level of accuracy in the fine resolution vorticity field. [Preview Abstract] |
Monday, November 21, 2011 11:22AM - 11:35AM |
H5.00005: Explicit Multirate Runge-Kutta Time Advancement for Navier-Stokes on Unstructured Grids Paul Covington, Frank Ham, Parviz Moin Unstructured grids of complex geometries often contain a handful of very small or poor quality elements that severely limit the global CFL-restricted timestep for explicit time advancement. So-called Multirate Runge-Kutta (MRK) methods attempt to overcome this limitation by using different time integration schemes in different regions of the domain based on a local stability criterion, thereby reducing overall computational cost (E. Constantinescu, JSC 2007 \& M. Schlegel, JCAM 2009). In this study, concepts from MRK are combined in a novel way to speedup an unstructured compressible finite volume code. As a validation case, the evolution of a 2D Euler vortex on a recursively refined grid will be presented. Algorithmic issues such as load balancing will also be discussed since these are crucial to approaching the theoretically achievable speedup. The practical implications of this technique will be demonstrated on a large-scale simulation of a low Mach number automotive fan. [Preview Abstract] |
Monday, November 21, 2011 11:35AM - 11:48AM |
H5.00006: Numerical simulation, prediction and experimental control of the dynamic behavior of a rotating magnetic particle chain Yang Gao, Tae Gon Kang, Martien Hulsen, Jaap den Toonder A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of magnetic particle chains in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chains which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a true description of the particle dynamics. A small error of deviation is observed when benchmarking the numerical scheme against the direct simulation method. The numerical results are compared with experiments showing good agreement both qualitatively and quantitatively. In addition, a dimensionless number is derived as the sole control parameter for the rotational bead chain dynamics. [Preview Abstract] |
Monday, November 21, 2011 11:48AM - 12:01PM |
H5.00007: One Possible Pitfall with Current Practice in Grid-Convergence Ryan Z. Davis, Richard Skifton, Akira Tokuhiro It is claimed that a possible flaw could exist in common-practice grid convergence studies. The problem comes when a field point value is observed near a discontinuity or a strong gradient and used to calculate the order-of-convergence, or even confirm grid convergence. A discrete domain can produce a ``smoothing'' effect in the vicinity of strong gradients. When field point values are observed near these areas their values can change dramatically, or not at all, depending on where the discrete points lie. This can lead the user to believe grid convergence has been achieved when in reality it has not. A submerged jet is used as a case study to demonstrate how the order-of-convergence can be affected when observing field point values near and far from strong gradients. [Preview Abstract] |
Monday, November 21, 2011 12:01PM - 12:14PM |
H5.00008: Toward 3D vortex methods with deforming basis functions Louis Rossi, Claudio Torres We present recent results extending methods for 2D vortex methods with deforming basis functions to three dimensions. Vortex methods are numerical schemes for approximating solutions to the Navier- Stokes equations using a linear combination of moving basis functions to approximate the vorticity field of a fluid. Typically, the basis function velocity is determined through a Biot-Savart integral applied at the basis function centroid. One outcome of rigorous analysis is an new naturally adaptive high order 2D method with elliptical Gaussian basis functions that deform as they move according to flow properties. This new class of methods is very unusual because the basis functions do not move with the physical flow velocity at the basis function centroid as is usually specified in vortex methods. The resulting analysis leads to deforming, ellipsoidal basis functions capable of achieving high spatial order. We now extend these results to three dimensions where traditional vortex methods suffer the additional shortcoming of not preserving the divergence of the vorticity field. We will discuss the latest results on our efforts to develop a complete 3D vortex method with adaptive, deforming blobs. [Preview Abstract] |
Monday, November 21, 2011 12:14PM - 12:27PM |
H5.00009: Fully explicit algorithms for fluid simulation Jonathan Clausen Computing hardware is trending towards distributed, massively parallel architectures in order to achieve high computational throughput. For example, Intrepid at Argonne uses 163,840 cores, and next generation machines, such as Sequoia at Lawrence Livermore, will use over one million cores. Harnessing the increasingly parallel nature of computational resources will require algorithms that scale efficiently on these architectures. The advent of GPU-based computation will serve to accelerate this behavior, as a single GPU contains hundreds of processor ``cores.'' Explicit algorithms avoid the communication associated with a linear solve, thus parallel scalability of these algorithms is typically high. This work will explore the efficiency and accuracy of three explicit solution methodologies for the Navier--Stokes equations: traditional artificial compressibility schemes, the lattice-Boltzmann method, and the recently proposed kinetically reduced local Navier--Stokes equations [Borok, Ansumali, and Karlin (2007)]. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 21, 2011 12:27PM - 12:40PM |
H5.00010: Analysis of boundary conditions and diffusion schemes for SPH methods Zhenyu He, Louis Rossi In this paper, we systematically explore the accuracy and stability of different methods for satisfying boundary conditions and capturing viscous diffusion in smoothed particle hydrodynamics (SPH). Smoothed particle hydrodynamics (SPH) is a Lagrangian method for compressible and incompressible flows. The state of fluid system is represented by a set of moving basis functions which interpolate the material properties. The mesh-free formulation of the method and its inherent stability make it popular for problems that have complex geometry or large deformations. Our research focuses mathematically on an accurate and efficient treatment for physical boundary conditions. Also, we analyze several smoothing kernels and diffusion schemes. We compare different techniques for non-slip, non-penetration conditions such as fixed fluid particles, ghost particles and boundary particle forces. We verify our results by comparing computations to exact solutions for 2D planar and circular, steady and unsteady Couette flows. [Preview Abstract] |
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