Wavelet-based Adaptive Techniques Applied to Turbulent Hypersonic Scramjet Intake Flows

The simulation of hypersonic flows is computationally demanding due to large gradients of the flow variables caused by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely small cells in the respective regions. Taking turbulence into account intensives the variation in scales even more. Furthermore, hypersonic flows have been shown to be extremely grid sensitive. For the simulation of three-dimensional configurations of engineering applications, this results in a huge amount of cells and prohibitive computational time. Therefore, modern adaptive techniques can provide a gain with respect to computational costs and accuracy, allowing the generation of locally highly resolved flow regions where they are needed and retaining an otherwise smooth distribution. An h-adaptive technique based on wavelets is employed for the solution of hypersonic flows. The compressible Reynolds averaged Navier-Stokes equations are solved using a differential Reynolds stress turbulence model, well suited to predict shock-wave-boundary-layer interactions in high enthalpy flows. Two test cases are considered: a compression corner and a scramjet intake. The compression corner is a classical test case in hypersonic flow investigations because it poses a shock-wave-turbulent-boundary-layer interaction problem. The adaptive procedure is applied to a two-dimensional confguration as validation. The scramjet intake is firstly computed in two dimensions. Subsequently a three-dimensional geometry is considered. Both test cases are validated with experimental data and compared to non-adaptive computations. The results show that the use of an adaptive technique for hypersonic turbulent flows at high enthalpy conditions can strongly improve the performance in terms of memory and CPU time while at the same time maintaining the required accuracy of the results.Comment: 26 pages, 29 Figures, submitted to AIAA Journa

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Multiresolution analysis as an approach for tool path planning in NC machining

Wavelets permit multiresolution analysis of curves and surfaces. A complex curve can be decomposed using wavelet theory into lower resolution curves. The low-resolution (coarse) curves are similar to rough-cuts and high-resolution (fine) curves to finish-cuts in numerical controlled (NC) machining.;In this project, we investigate the applicability of multiresolution analysis using B-spline wavelets to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary similar to conventional offsetting, while lower resolution curves, straight lines and circular arcs are used farther away from the object boundary.;Experimental results indicate that wavelet-based multiresolution tool path planning improves machining efficiency. Tool path length is reduced, sharp corners are smoothed out thereby reducing uncut areas and larger tools can be selected for rough-cuts

Multiresolution editing for B-spline curves and surfaces

Since 1980 surface modeling has been used in industrial design, CAD and entertainment to create and represent complex forms. Even with this comparatively long history of development, challenges remain in free-form surface modeling. One such challenge is building surface creation and editing techniques that effectively balance the need for local control with the need to control the overall global shape, or sweep of the surface. This dissertation presents a multiresolution approach to the creation of surfaces that allows a designer to more easily manage this balance between local and global control. The techniques presented in this dissertation utilize a wavelet decomposition of B-spline curves and surfaces to allow a designer to easily develop the basic shape using lower level representations, and then seamlessly switch to higher level representations to achieve fine control over local features. The algorithms described in the dissertation are implemented in an interactive software system that is used to demonstrate their effectiveness in comparison to existing methods

Constraints on crustal rheology and age of deformation from models of gravitational spreading in Ishtar Terra, Venus

Gravitational spreading is expected to lead to rapid relaxation of high relief due to the high surface temperature and associated weak crust on Venus. In this study, we use new Magellan radar and altimetry data to determine the extent of gravitational relaxation in Ishtar Terra, which contains the highest relief on Venus as well as areas of extremely high topographic slope. Within Ishtar Terra the only mountain belts found on Venus, Akna, Danu, Freyja, and Maxwell Montes, nearly encircle the smooth, high (3-4 km) plateau of Lakshmi Planum. Finite-element models of this process give expected timescales for relaxation of relief and failure at the surface. From these modeling results we attempt to constrain the strength of the crust and timescales of deformation in Ishtar Terra. Below we discuss observational evidence for gravitational spreading in Ishtar Terra, results from the finite-element modeling, independent age constraints, and implications for the rheology and timing of deformation

Real-time Photorealistic Visualisation of Large-scaleMultiresolution Terrain Models

Height field terrain rendering is an important aspect of GIS, outdoor virtual reality applicationssuch as flight simulation, 3-D games, etc. A polygonal model of very large terrain data requiresa large number of triangles. So, even most high-performance graphics workstations have greatdifficulty to display even moderately sized height fields at interactive frame rates. To bringphotorealism in visualisation, it is required to drape corresponding high-resolution satellite oraerial phototexture over 3-D digital terrain and also to place multiple collections of point-location-based static objects such as buildings, trees, etc and to overlay polyline vector objects suchas roads on top of the terrain surface. It further complicates the requirement of interactive framerates while navigation over the terrain. This paper describes a novel approach for objects andterrain visualisation by combination of two algorithms, one for terrain data and the other forobjects. The terrain rendering is accomplished by an efficient dynamic multiresolution view-dependent level-of-detail mesh simplification algorithm. It is augmented with out-of-corevisualisation of large-height geometry and phototexture terrain data populated with 3-D/2-Dstatic objects as well as vector overlays without extensive memory load. The proposedmethodology provides interactive frame rates on a general-purpose desktop PC with OpenGL-enabled graphics hardware. The software TREND has been successfully tested on different real-world height maps and satellite phototextures of sizes up to 16K*16K coupled with thousandsof static objects and polyline vector overlays