Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session KB: Computational Fluid Dynamics V |
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Chair: James Brasseur, Pennsylvania State University Room: Salt Palace Convention Center 150 D-F |
Tuesday, November 20, 2007 8:00AM - 8:13AM |
KB.00001: Construction of Perfectly Matched Layer in cylindrical coordinates with non-zero mean flow Sarah Parrish, Fang Hu Non-reflecting boundary condition is an essential component in developing computational fluid dynamics (CFD) and computational aeroacoustics (CAA) algorithms. Perfectly Matched Layer (PML) is a technique for developing non-reflecting boundary conditions. PML for linearized Euler equations, as well as its extension to the nonlinear Euler and Navier-Stokes equations, have been developed recently for computational grid in the Cartesian coordinates. In this work, PML for the Euler equations in polar coordinates will be presented. The central issue is the stability of the polar PML in the presence of a mean flow. A space-time transformation is utilized to modify the dispersion relations of the linear waves in the derivation process. A stability analysis is carried out for the PML equations in the polar coordinates. An added benefit of PML in the polar coordinates is that a mean flow in an arbitrary can be treated easily. Numerical examples will also be presented to demonstrate the validity and stability of the newly developed PML equations. [Preview Abstract] |
Tuesday, November 20, 2007 8:13AM - 8:26AM |
KB.00002: A One-Dimensiontal Conservative Method to Track Contact Discontinuities in a Compressible Media Caroline Gatti-Bono We present a one-dimensional algorithm to track an interface between two compressible media. The method can readily be extended to multiple dimensions. The moving interface cuts out time-varying control volumes and a consistent finite-volume discretization is derived by applying the divergence theorem in space-time. The method is fully conservative, even at the discontinuity, and the truncation error is expected to be first-order at the boundary between the two fluids, which is one order higher than conventional methods. Classical benchmark results and convergence studies are presented. [Preview Abstract] |
Tuesday, November 20, 2007 8:26AM - 8:39AM |
KB.00003: Moment-of-Fluid Method in Action Hyung Taek Ahn, Mikhail Shashkov Moment-of-fluid (MoF) method, a new volume-tracking multi-material/multi-phase flow simulation method, is presented. Contrast to the Volume-of-Fluid (VoF) method that uses only volume fraction data for advection and interface reconstruction, the MoF method utilizes moment data, namely the volume fraction as well as the centroid of each material in the mixed cells (i.e. cells containing multiple materials). Based on the the moment data of each material, the material interfaces are reconstructed with second order accuracy in a strictly conservative manner. The MoF method is coupled with Stabilized Finite Element based incompressible Navier-Stokes solver for two materials. The effectiveness of MoF method is demonstrated with several test cases including Rayleigh-Taylor instability, rising bubble, and broken dam problems. [Preview Abstract] |
Tuesday, November 20, 2007 8:39AM - 8:52AM |
KB.00004: A Fully Implicit, Conservative, Front Tracking Method for All-Speed Multi-fluid Flows Robert Nourgaliev, Vincent Mousseau, Dana Knoll A novel front-tracking method is developed for simulation of compressible all-speed multi-fluid flows. The prominent features of our method are: $a)$ it is \textit{fully implicit}, based on Jacobian-Free Newton-Krylov (JFNK) framework, opening the possibility to efficiently simulate multi-physics problems with a wide spread in time scales; $b)$ it is \textit{fully conservative}, even near the contacts, without any adverse consequences with pressure/velocity oscillations; $c)$ hybridization of the Eulerian treatment in the bulk-fluid with the semi-Lagrangian treatments of cut-cells near multi-material interfaces enables \textit{efficient high-order-accurate} \textit{spatial discretization}, capturing interfacial jumps sharply, within one cell; $d)$ \textit{interfacial geometry} \textit{is a part of the JFNK solution vector}, avoiding operator-split treatment of the interface and near-interfacial fluid flows, which is a state-of-the-art in all previous (explicit) methods for interface tracking. We discuss and demonstrate the effectiveness of the Implicit Continuous-fluid Eulerian (ICE) physics-based preconditioner (PBP) of the Krylov (GMRES) method used as a linear solver in our Newton-based implicit Runge-Kutta time discretization. It will be shown that the ICE-PBP collapses all generally-complex eigenvalues of the Jacobian matrix to the real axes, effectively clustering eigenvalues and thus enabling a significant speed-up of convergence of the linear solver. [Preview Abstract] |
Tuesday, November 20, 2007 8:52AM - 9:05AM |
KB.00005: Efficient Analysis of Stochastic Systems in the Presence of Discontinuity Tonkid Chantrasmi, Alireza Doostan, Gianluca Iaccarino This talk presents the predictive accuracy of some existing uncertainty propagation schemes for solution of stochastic partial differential equations that exhibit certain irregularities in the probability space. In particular, it will be shown that traditional global stochastic Galerkin schemes, such as polynomial chaos expansions, are inefficient in capturing quantities of interest that are discontinuous in the random space due to Gibbs phenomenon. As one possibility, the formalism of Pade approximation of discontinuous functions coupled with a stochastic collocation scheme is proposed to resolve the above issue for the steady state solution of a dual throat nozzle. The initial velocity prescribed on the domain of the system is modeled as a high- dimensional random field. The goal of the analysis is then to efficiently estimate the probability distribution function of the shock location in the steady state regime given such uncertainty in the initial velocity. The advantages of the proposed algorithm over the existing techniques for capturing discontinuities in both physical space and also a high- dimensional probability space will be discussed in details. [Preview Abstract] |
Tuesday, November 20, 2007 9:05AM - 9:18AM |
KB.00006: Evaluation of general non-reflecting boundary conditions for industrial CFD applications Branislav Basara, Sergei Frolov, Boris Lidskii, Vladimir Posvyanskii The importance of having proper boundary conditions for the calculation domain is a known issue in Computational Fluid Dynamics (CFD). In many situations, it is very difficult to define a correct boundary condition. The flow may enter and leave the computational domain at the same time and at the same boundary. In such circumstances, it is important that numerical implementation of boundary conditions enforces certain physical constraints leading to correct results which then ensures a better convergence rate. The aim of this paper is to evaluate recently proposed non-reflecting boundary conditions (Frolov et al., 2001, Advances in Chemical Propulsion) on industrial CFD applications. Derivation of the local non-reflecting boundary conditions at the open boundary is based on finding the solution of linearized Euler equations vanishing at infinity for both incompressible and compressible formulations. This is implemented into the in-house CFD package AVL FIRE and some numerical details will be presented as well. The key applications in this paper are from automotive industry, e.g. an external car aerodynamics, an intake port, etc. The results will show benefits of using effective non-reflecting boundary conditions. [Preview Abstract] |
Tuesday, November 20, 2007 9:18AM - 9:31AM |
KB.00007: Role of Subfilter-Scale Model Anisotropy on Large-Eddy Simulation of the Neutral Atmospheric Boundary Layer Tie Wei, James Brasseur A long-standing problem in large eddy simulation of neutral atmospheric boundary layer with eddy viscosity models is the over-prediction of mean shear near the surface. The near-surface errors arise from a mix of numerical and subfilter-scale (SFS) model issues at the first several grid levels, where integral scales are necessarily under-resolved and the turbulence is highly anisotropic. Here we study the role of SFS stress anisotropy by manipulating the traditional scalar (isotropic) eddy viscosity. In a numerical experiment we reduced the eddy viscosity for the diagonal SFS fluxes while keeping the traditional ones for the off-diagonal SFS fluxes. With the modified anisotropic SFS model the over-prediction of mean shear was reduced, the streamwise velocity variance was reduced and the vertical velocity variance was increased. There were also significant differences in the 2D horizontal energy spectra between the traditional and modified models. The modified models were less dissipative than the traditional ones. We aim to determine the underlying physical mechanisms that underlie the relationship between the anisotropic properties of SFS model and prediction. [Preview Abstract] |
Tuesday, November 20, 2007 9:31AM - 9:44AM |
KB.00008: Investigations of vortex-cylinder mechanism of interaction using URANS and LES Marcel Ilie Numerical simulations of a single vortex superimposed on a uniform flow past a circular cylinder were performed using both unsteady Reynolds-averaged Navier-Stokes equations (URANS) and large eddy simulation (LES) techniques for relatively high Reynolds number flows, Re = 1.4x10$^{6}$. Vortex-structure interaction flow phenomena are very common in many engineering applications, such as aircraft at high angle of attack, flow past landing gear, blade-vortex interaction for rotorcraft, etc. The vortex-structure interaction phenomenon is of critical importance due to the inheriting danger associated with the vortex induced vibrations. In the present analysis, parametric investigations were performed for different test cases, based on both the vortex-cylinder horizontal miss distance and the sense of vortex rotation. The URANS approach fails to accurately predict the unsteady flow field due to excessive dissipation. The LES technique provides a promising tool for obtaining the unsteady wall-pressure fields, aerodynamic coefficients and the acoustic source functions. From the present analysis using LES, it was observed that the presence of the vortex in the flow field causes an increase of the Strouhal number value. Also, the present analysis showed that the vortex-cylinder horizontal miss-distance influences the mechanism of interaction and implicitly the aerodynamic coefficients. [Preview Abstract] |
Tuesday, November 20, 2007 9:44AM - 9:57AM |
KB.00009: Effective Numerical Viscosity in Spectral Multidomain Penalty Method-Based Simulations of Turbulence Y.C. Lin, Peter Diamessis, Julian Domaradzki Numerical methods used to simulate turbulence often employ, explicitly or implicitly, a variety of procedures to control numerical instabilities, introducing in the process unquantifiable dissipation of numerical origin. We describe a methodology that allows to assess such a numerical dissipation on an example of a specific, spectral multidomain method developed for the simulation of high Reynolds number turbulence. The temporal discretization ensures maximum temporal accuracy by combining third order stiffly stable and backward differentiation schemes with a high-order boundary condition for the pressure. In the non-periodic vertical direction, a spectral multidomain discretization is used and its stability is ensured through use of penalty techniques, spectral filtering and strong adaptive interfacial averaging. We show that the effects of stabilizers can be quantified in terms of the numerical viscosity and we find that it can be comparable, and sometimes larger, than the physical viscosity. Away from domain interfaces and boundaries the stabilizers have an expected dissipative character but a strong anti-dissipative character is observed at the interfaces. We attribute this behavior to the way the penalty method prevents catastrophic Gibbs' oscillations, providing the flow variables freedom to adjust by relaxing the interface conditions. [Preview Abstract] |
Tuesday, November 20, 2007 9:57AM - 10:10AM |
KB.00010: Explanation for the Incorrect Prediction of Mean Velocity Gradient Near Surfaces in LES of Shear-dominated Boundary layers J. Brasseur, T. Wei In 1992 Mason \& Thomson pointed out that LES of high Reynolds number wall bounded shear flows with eddy viscosity SFS closures produces an overshoot in mean shear near surfaces. In the 15 intervening years several studies have attempted to adjust the SFS model to eliminate the overshoot, but none have been entirely successful, primarily because the reason for the overshoot is largely not understood. We believe we have successfully explained the overshoot and the basic issues that must be addressed to eliminate it. Using basic near-surface scaling arguments for DNS vs. LES of turbulent channel flow, we show that, like the inertial vs. viscous stress near a smooth wall, the SFS stress generally dominates resolved stress at the first few grid levels for multiple reasons, including inherent under-resolution of the integral scales by the grid. A numerical ``viscous layer'' is established with eddy viscosity closures that introduces a noninertial scaling and leads to the overshoot. We introduce a ``LES Reynolds number'' ($Re^{LES}$) and show that $Re^{LES}$ includes grid resolution, grid aspect ratio, and model constant. Three criteria must be met: (1) a minimum $Re^{LES}$ to maintain turbulence, (2) a larger $Re^{LES}$ to properly resolve the inertial layer and, finally, (3) a yet larger $Re^{LES}$ to eliminate the overshoot. We show that the final criterion can only be met by adjusting grid aspect ratio together with model constant. [Preview Abstract] |
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