Gordon Erlebacher

The analysis and modelling of dilatational terms in compressible turbulence

It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

A novel technique for face recognition using range imaging

We consider a novel technique for recognizing people from range images (RI) of their faces. Range images have the advantage of capturing the shape variation irrespective of illumination variabilities. We describe a procedure for generating RI effaces using data from a 3D scanner, and registering them in the image plane by aligning salient facial features. For statistical analysis of RI, we use standard projections such as PCA and ICA, and then impose probability models on the coefficients. An experiment describing recognition effaces using the FSU 3D face database is presented.

High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster

We implement a high-order finite-element application, which performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA Tesla graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. Contrary to many finite-element implementations, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. We discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We use mesh coloring to efficiently handle summation operations over degrees of freedom on an unstructured mesh, and non-blocking MPI messages in order to overlap the communications across the network and the data transfer to and from the device via PCIe with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x.

The subgrid‐scale modeling of compressible turbulence

A subgrid‐scale model recently derived by Yoshizawa [Phys. Fluids 29, 2152 (1986)] for use in the large‐eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is only applicable to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre‐filtered fields, is suggested which appears to reduce these limitations.

Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA

We port a high-order finite-element application that performs the numerical simulation of seismic wave propagation resulting from earthquakes in the Earth on NVIDIA GeForce 8800 GTX and GTX 280 graphics cards using CUDA. This application runs in single precision and is therefore a good candidate for implementation on current GPU hardware, which either does not support double precision or supports it but at the cost of reduced performance. We discuss and compare two implementations of the code: one that has maximum efficiency but is limited to the memory size of the card, and one that can handle larger problems but that is less efficient. We use a coloring scheme to handle efficiently summation operations over nodes on a topology with variable valence. We perform several numerical tests and performance measurements and show that in the best case we obtain a speedup of 25.

The analysis and simulation of compressible turbulence

This paper considers compressible turbulent flows at low turbulent Mach numbers. Contrary to the general belief that such flows are almost incompressible (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a nondimensional time scale which is the order of the fluctuating Mach number. An asymptotic theory which enables a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

INTERACTION OF A SHOCK WITH A LONGITUDINAL VORTEX

In this paper we study the shock/longitudinal vortex interaction problem in axisymmetric geometry. Linearized analysis for small vortex strength is performed, and compared with results from a high order axisymmetric shock-fitted Euler solution obtained for this purpose. It is confirmed that for weak vortices, predictions from linear theory agree well with results from nonlinear numerical simulations at the shock location. To handle very strong longitudinal vortices, which may ultimately break the shock, we use an axisymmetric high order essentially non-oscillatory (ENO) shock capturing scheme. Comparison of shock-captured and shock-fitted results are performed in their regions of common validity. We also study the vortex breakdown as a function of Mach number ranging from 1.3 to 10, thus extending the range of existing results. For vortex strengths above a critical value, a triple point forms on the shock and a secondary shock forms to provide the necessary deceleration so that the fluid velocity can adjust to downstream conditions at the shock.

Lagrangian-Eulerian advection of noise and dye textures for unsteady flow visualization

A new hybrid scheme, called Lagrangian-Eulerian advection (LEA), that combines the advantages of the Eulerian and Lagrangian frameworks is applied to the visualization of dense representations of time-dependent vector fields. The algorithm encodes the particles into a texture that is then advected. By treating every particle equally, we can handle texture advection and dye advection within a single framework. High temporal and spatial correlation is achieved through the blending of successive frames. A combination of particle and dye advection enables the simultaneous visualization of streamlines, particle paths and streak-lines. We demonstrate various experimental techniques on several physical flow fields. The simplicity of both the resulting data structures and the implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

High-order ENO schemes applied to two- and three-dimensional compressible flow

Abstract High-order essentially non-oscillatory (ENO) finite-difference schemes are applied to the two- and three-dimensional compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both non-oscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

A texture-based framework for spacetime-coherent visualization of time-dependent vector fields

We propose unsteady flow advection-convolution (UFAC) as a novel visualization approach for unsteady flows. It performs time evolution governed by pathlines, but builds spatial correlation according to instantaneous streamlines whose spatial extent is controlled by the flow unsteadiness. UFAC is derived from a generic framework that provides spacetime-coherent dense representations of time dependent-vector fields by a two-step process: 1) construction of continuous trajectories in spacetime for temporal coherence; and 2) convolution along another set of paths through the above spacetime for spatially correlated patterns. Within the framework, known visualization techniques-such as Lagrangian-Eulerian advection, image-based flow visualization, unsteady flow LIC, and dynamic LIC-can be reproduced, often with better image quality, higher performance, or increased flexibility of the visualization style. Finally, we present a texture-based discretization of the framework and its interactive implementation on graphics hardware, which allows the user to gradually balance visualization speed against quality.