Richard Sanders, Ph.D., Associate Professor, Mathematics, UH
The numerical solution of the equations that govern hypersonic flow remains one of the most challenging problems in modern engineering. Features characteristic of hypersonic flow include:
During spacecraft reentry, a space vehicle typically encounters flow speeds in excess of Mach 20. The spacecraft designer must accurately predict flow conditions at these extreme speeds for reasons of economy and, more importantly, for the safety of the crew and vehicle. However, these conditions can not be reliably predicted by ground-based wind tunnel experiments. Hence. numerical simulation of the hypersonic flow environment is the only reasonable alternative.
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Figure 1. Demonstration of grid size independent convergence rate for the UH multigrid method applied to a 2D multicomponent Stefan-Maxwell diffusion equation. (Left and right figures correspond to a different set of diffusion coefficients.) Plots depict residual versus the number of multigrid iterations. Five grid sizes in each figure range from 81 to 16641 nodes.
Over the last several years, I have worked in close cooperation with scientists at NASA/JSC to improve their existing techniques for finding steady state solutions to the equations that govern hypersonic flow. In the NASA/JSC three-dimensional finite difference code used to simulate spacecraft reentry, typically over one million grid points are utilized. A single simulation can take over one day of CPU time on on a Cray YMP supercomputer. The primary factor that explains this poor performance is the underlying iterative method used to compute the steady state and not the work required to spatially discretize the problem. Thousands of iterations of a pseudo implicit, time marching scheme are required in the traditional NASA code. For these difficult flow problems in the hypersonic regime, however, no other technique, in general, has to date been shown to be more efficient.
Significant progress has been made on this problem during the course of the investigation. A new multigrid technique was developed specifically for application to hypersonic flow. Two issues were identified that caused earlier multigrid solution techniques to fail when applied to hypersonic flow problems. The first was the strong anisotropic nature of these flows. The second was the difficulty reducing the iterative error within the numerical shock layer. With these issues identified, a new multigrid technique was developed for finding steady solutions to scalar nonlinear multidimensional conservation laws. Numerical experiments yield machine epsilon convergence to steady state in ten to fifteen iterations. Moreover, the convergence rate offered by the new technique is completely independent of the spatial grid refinement. These results have been justified by theoretical considerations. These techniques are being extended to work in progress on multidimensional systems of conservation laws.
Figure 2. The body surface of a computational grid used to calculate
hypersonic flow around the US shuttle.
During the current investigation, an efficient and robust multigrid technique was also developed for finding steady solutions to flows with significant multicomponent diffusion modeled by Stefan-Maxwell diffusion. Again, machine epsilon convergence to steady state is obtained in ten to fifteen multigrid iterations.
A portion of the investigation was devoted to the design and construction of the Houston High Speed Flow Database. This network database will contain computational and experimental data for a wide range of standardized hypersonic test problems. A large volume of data has already been collected from cooperating scientists in Europe, Russia and Japan.
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William R. Sheldon, Professor, Physics, UH
ULTRAVIOLET (UV) RAYS-Dotted lines are the UV flux at the surface of an Earth-like planet orbiting a hotter (F2V) and a cooler (K2V) star compared to the Earth and our sun; solid lines are the UV flux at the top of the planetary atmosphere. The detailed photochemical calculation indiates that all three planets would be habitable, thus refuting an earlier suggestion that the planet orbiting the cooler star would be bombarded by more UV radiation than a biota could tolerate.
A computer program designed to study the photochemistry of the atmosphere has been installed in the UH Space and Atmospheric Physics Group and is currently undergoing check-out. Support from ISSO provided funding for a graduate student to work part-time on this project, enabling the utilization of the computer program developed by Prof. J. F. Kasting of Pennsylvania State University in the 1980s. Prof. Kasting's computer program describes the photochemistry of the atmosphere with the solar radiation spectrum as the input. Concentrations as a function of altitude in an atmosphere containing nitrogen, oxygen, hydrogen, and carbon compounds are listed, along with the reaction rates and absorption cross-sections of the species of importance.
The program next calculates the radiation spectrum at the Earth's surface after modification by traversing the atmosphere. In consultation with Prof. Kasting, the program is currently being updated to rid it of obsolences and to input current atmospheric findings.
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Leang S. Shieh, Ph.D., Professor, Electrical and Computer Engineering, UH
Most models of physical systems are formulated by a continuous-time uncertain framework, for which well-established robust control methods are available. The uncertainties in these systems arise from unmodeled dynamics, parameter variations, sensor noises, actuator constraints, etc. These variations do not follow any of the known probability distributions in general, and are most often quantified in terms of amplitude and/or frequency bounds. Hence, the practical systems are most suitably represented by continuous-time interval models with bounded parameters, disturbances and noise inputs. However, at present, neither an effective method nor software is available for digital modeling and digital simulation of continuous-time interval systems.
For significantly improving properties of the uncertain system represented by a continuous-time uncertain state-space framework, analogue robust control design methods exist. With rapid advances in digital technology and computers, operators need a complementary analogue robust controller implemented with a digital controller for better reliability at lower cost, more flexibility, and better performance. The process of converting an analogue controller into an equivalent digital controller, so that the states of the digitally controlled sampled-data system closely match those of the original continuous-time controlled system for a relatively longer sampling period, is called "state-matching digital redesign." Several state-matching digital redesign methods are available for digital control of continuous-time nominal systems. However, at present, no effective method is available for digital redesign of sampled-data interval systems.
The main accomplishments of our current work are three-fold:
More precisely, we develop a scaling and squaring geometric series method together with interval arithmetic to convert a continuous-time interval system into an equivalent discrete-time interval model. The model constructed, guaranteed to tightly enclose the precise original interval model, can be utilized for digital simulation and digital design of continuous-time uncertain system.1
Also, we developed a new digital redesign method together with interval arithmetic to discretize the predesigned continuous-time H2/H∞ controller for robust digital control of the continuous-time uncertain systems. The resulting robust digital controller is able to closely match the states of the digitally controlled sampled-data uncertain system with those of the original continuous-time controlled uncertain system for a relatively longer sampling period.2
Moreover, we developed a state-feedback robust control law for the mismatching or matching of uncertain linear Lagrange's system, with structured or unstructured uncertainties. The designed closed-loop systems possess the properties of robust pole-clustering within a vertical strip and disturbance rejection with an H∞-norm constraint.3
References
1Shieh, L. S., X. Zou, and N. P. Coleman. "Digital Interval Model Conversion and
Simulation of Continuous-time Uncertain Systems," IEE Proc., Part D., Control Theory
and Applications 142.4 (1995): 315-22.
2Shieh, L. S., W. M. Wang, and J. S. H. Tsai. "Digital Modelling and Digital Redesign
of Sampled-data Uncertain Systems," IEEE Proc., Part D., Control Theory and
Applications 142 (1995): 585-94.
3Wang, S. G., L. S. Shieh, and J. W. Sunkel. "Robust Optimal Pole-Clustering in a
Vertical Strip and Disturbance Rejection for Uncertain Lagrange's Systems," Dynamics
and Control 5.3 (1995): 295-312.
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Liwen Shih, Ph. D., Associate Professor, Computer Engineering, School of Natural and Applied Sciences, UHCL
Digital image processing techniques through texture analysis have been of prime interest in both macroscopic digital image data set analysis (Landsat imagery of NASA) and microscopic image analysis, particularly in medical applications, which use texture parameters on digitized image data for enhanced cancer detection for ultrasound images of liver and kidney diseases and for breast cancer from mammograms of X-ray image data. The resolution of medical image data is a challenging task in texture algorithms. For this reason, implementation of texture algorithms in-volves intense computational complexity in processing the image data.
The accuracy of current visual interpretation methods for identifying the presence of cancer from prostate ultrasound images is about 40 percent. Earlier image classification investigations (Premkumar, Houston) show a promise of a two fold increase in accuracy, up to 80 percent, in identifying the presence of cancer from the same image data. In the current study, prostate ultrasound image data are being explored for purposes of implementing texture analysis algorithms to develop image processing technique for enhanced and early prostate cancer detection.
The most optimal system of texture analysis will utilize recent advancements in parallel processing systems. Access to an IBM SP1 computer in summer of 1994 enabled exploration of such systems for image analysis, particularly texture analysis, and proved it a promising technology. Currently, we are using Connection Machine CM5 with up to 3,200 PEs to enhance the performance of the texture analysis code (see Table 1). With massively parallel systems, it may even be possible to see near realtime conclusions of the texture analysis for predicting or identifying prostate cancer lesions. Such an objective procedure for detecting the most common cancer in men is not available with reliable accuracy.
Table 1. Performance improvement.
| Machine | VAX Micro 3400 | Cm-5 |
| No. of Processors | 1 | 128 |
| CPU time/image | 8 days | 40 min-1 hr. |
| CPU time/20 images | 160 days | 13.3-20 hr. |
Contents
ISSO -- Institute for Space Systems Operations
1994-1995 Annual Report
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