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NONITERATIVE PARABOLIC GRID GENERATION FOR PARABOLIZED EQUATIONS

AIAA JOURNAL 1987年第4期25卷 542-549页

作者： HODGE, JK LEONE, SA MCCARTY, RL Air Force Institute of Technology Wright-Patterson Air Force Base Ohio

Three-dimensional generalized curvilinear grids are generated for Cartesian, cylindrical, and spherical shaped bodies using parabolic partial differential equations. Elliptic grid equations are parabolized in an axial direction consistent with the Parabolized Navier Stokes (PNS) equations or the boundary-layer equations. The parabolized grid equations are solved in a noniterative fashion by marching in two directions. Any limitations of parabolic grid generation are investigated on convex and concave corners. Even though body surfaces are not smooth, the grid between axial stations is smoothed. Highly stretched and optimized grids for high Reynold's number are accurately and efficiently generated for the first time using parabolic grid equations with a difference approximation based on exponentials. The grid can also be adapted easily based on a flow solution at the previous axial station using this approach. © 1987 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Boundary Layer Equations Poisson's Equation Turbulent Flow Velocity Profiles finite difference approximation Cartesian Coordinate System Solution Algorithm Iterative Solution Computer Memory Flow Equations

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Robust numerical method for a system of singularly perturbed parabolic reaction-diffusion equations on a rectangle

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MATHEMATICAL MODELLING AND ANALYSIS 2008年第2期13卷 251-261页

作者： Shishkina, L. Shishkin, G. Russian Acad Sci Inst Math & Mech Ekaterinburg 620219 Russia

A Dirichlet problem is considered for a system of two singularly perturbed parabolic reaction-diffusion equations on a rectangle. The parabolic boundary layer appears in the solution of the problem as the perturbation parameter epsilon tends to zero. On the basis of the decomposition solution technique, estimates for the solution and derivatives are obtained. Using the condensing mesh technique and the classical finite difference approximations of the boundary value problem under consideration, a difference scheme is constructed that converges epsilon-uniformly at the rate O(N-2 ln(2) N + N-0(-1)), where min(s) N-s, s = 1,2, N-s + 1 and N-0 + 1 are the numbers of mesh points on the axis x(s) and on the axis t, respectively.

关键词： initial-boundary value problem problem on a rectangle perturbation parameter epsilon system of parabolic equations reaction-diffusion equations finite difference approximation parabolic boundary layer decomposition solution technique a priori estimates epsilon-uniform convergence

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Vibration Energy Transfer Characteristics of Panels with Multiple Coupling Forms in Satellites

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INTERNATIONAL JOURNAL OF AERONAUTICAL AND SPACE SCIENCES 2023年第5期24卷 1231-1243页

作者： Shen, Yan Xu, Yang Sheng, Xiaowei Wan, Song Yin, Xianbo Donghua Univ Coll Mech Engn Shanghai 201620 Peoples R China Chinese Acad Sci Innovat Acad Microsatellites Shanghai 201620 Peoples R China

Micro-vibrations on-board a satellite have degrading effects on the performance of certain payloads like observation cameras. There are numerous sources and extremely complicated transfer paths for micro-vibration in satellites. The vibration energy transfer characteristics of panels with multiple coupling forms in satellites were analyzed, which can guide the vibration isolation measures of satellites. First, the satellite was divided into honeycomb panel subsystems with multiple coupling forms. In the next phase, based on the energy finite element analysis (EFEA), the energy finite element equation of the honeycomb subsystem and the connection matrix at the coupling boundary was established to determine the energy distribution and energy flow characteristics of the multiform coupled honeycomb panels under different excitation frequencies. Finally, the finite difference approximation based on the response obtained from the measurement point array was employed to obtain the energy density. By comparing the results of the experiment and EFEA simulation under different frequency excitations, the average error of the energy density was less than 4 dB, which proved the accuracy of EFEA in the transfer characteristics analysis of the vibration energy of the satellite. The experiment method of vibration transfer based on the finite difference approximation can directly obtain the energy density of the structure.

关键词： Satellite frame Vibration energy Transfer characteristics Energy finite element analysis finite difference approximation

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SOLUTION-ADAPTIVE GRID GENERATION USING PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS

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AIAA JOURNAL 1990年第6期28卷 1016-1023页

作者： NOACK, RW ANDERSON, DA The University of Texas at Arlington Arlington Texas

A solution-adaptive parabolic grid generation scheme has been developed. A new upwind finite-volume formulation for space marching solution of the steady Euler equations is also presented. In addition, a solutionadaptive elliptic grid scheme developed previously and applied to unsteady flow solutions is applied in the present steady-flow context. Solutions for hypersonic flow are computed with the present finite-volume formulation coupled to both the parabolic and elliptic adaptive grid schemes. The results show that the solution-adaptive parabolic scheme produces grids that track the flow features of interest as well as the elliptic grid procedure. This is significant because the parabolic procedure is much faster than an elliptic scheme producing a grid in an order of magnitude of less computational time. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Differential Equations Euler Equations Hypersonic Flows finite Volume Formulation Bow Shock Freestream Conditions finite difference approximation Re Entry Vehicle Angle of Attack Conservation of Mass

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ELECTRIC-DISCHARGE EXCITED BLAST WAVES IN A FLAT SUBSONIC NOZZLE

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AIAA JOURNAL 1993年第6期31卷 1060-1067页

作者： LUCHINI, P University of Naples Naples 80125 Italy

The persistence of pressure waves generated by an electric discharge in the throat of a subsonic nozzle is studied analytically and numerically with particular reference to the operation of the high-power EUREKA excimer laser under construction at the national Italian ENEA Frascati laboratories. The attention is focused on transverse waves traveling parallel to the discharge electrodes. After some analytical estimates, a quasi-two-dimensional numerical simulation is presented of the propagation of these waves in the anticipated geometry of the discharge chamber of the EUREKA laser. The possibility of reflection of pressure waves on the thermal slug left behind by the previous discharge is also considered.

关键词： Convergent Divergent Nozzles Flow Velocity Numerical Simulation Excimer Lasers Numerical Analysis Bessel Functions Convection Equations of Fluid Dynamics finite difference approximation Acoustic Wave Equation

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Unsteady Heat Transfer on Turbine Blades

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1990年第1期4卷 47-52页

作者： Cebeci, Tuncer Simoneau, Robert J. Platzer, Max F. Calif State Univ Long Beach Dept Aerosp Engn Long Beach CA 90840 USA NASA Lewis Res Ctr Heat Transfer Branch Cleveland OH USA Naval Postgrad Sch Dept Aeronaut Monterey CA USA

This paper describes a method for calculating heat transfer on turbine blades subjected to passing wakes. It is based on the numerical solution of the boundary-layer equations for laminar, transitional, and turbulent flows with a novel procedure to account for the movement of the stagnation point. Results are presented for a model flow and show that the procedure is numerically sound and produces results that can give good agreement with measurements provided that the turbulence model is adequate.

关键词： Heat Transfer Measurements Turbine Blades Turbulent Prandtl Number Blade Passing Frequency Turbulent Flow Kinematic Viscosity Incompressible Boundary Layer finite difference approximation Strouhal Number Prandtl Number

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A numerical modelling for the extraction of decay regions from color images of monuments

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MATHEMATICS AND COMPUTERS IN SIMULATION 2009年第8期79卷 2334-2344页

作者： Cerimele, Maria Mercede Cossu, Rossella CNR Ist Applicaz Calcolo Mauro Picone I-00185 Rome Italy

An innovative application focused on the segmentation of decay zones from images of stone materials is presented. The adopted numerical approach to extract decay regions from the color images of monuments provides a tool that helps experts analyze degraded regions by contouring them. In this way even if the results of the proposed procedure depend on the evaluation of experts, the approach can be a contribution to improving the efficiency of the boundary detection process. The segmentation is a process that allows an image to be divided into disjoint zones so that partitioned zones contain homogeneous characteristics. The numerical method, used to segment color images, is based on the theory of interface evolution, which is described by the eikonal equation. We adopted the fast marching technique to solve the upwind finite difference approximation of the eikonal equation. The fast marching starts from a seed point in the region of interest and generates a front which evolves according to a specific speed function until the boundary of the region is identified. We describe the segmentation results obtained with two speed functions, attained by the image gradient computation and color information about the object of interest. Moreover, we present the extension of the working modality of the method by introducing the possibility to extract the regions not only in a local way but also in a global way on the entire image. In this case, in order to improve the segmentation efficiency the application of the fast marching technique starts with more seed points defined as seed regions. The study case concerns the impressive remains of the Roman Theatre in the city of Aosta (Italy). In the image segmentation process the color space L*a*b* is utilized. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Eikonal equation finite difference approximation Fast marching Segmentation Color image

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Sensitivity analysis for a structured juvenile-adult model

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2012年第3期64卷 190-200页

作者： Ackleh, Azmy S. Deng, Keng Yang, Xing Univ Louisiana Lafayette Dept Math Lafayette LA 70504 USA

In this paper, we consider a model which describes the dynamics of an amphibian population where individuals are divided into juveniles and adults. We derive sensitivity partial differential equations for the sensitivities of the solution with respect to the reproduction and mortality rates for adults. We also present numerical results to show the application of these equations to an amphibian population of green tree frogs (Hyla cinerea): (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Structured juvenile-adult model Sensitivity equations finite difference approximation

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Effects of thermal conductivity and geometry of materials on the temperature variation in packed bed solar air heater

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JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY 2013年第1期111卷 839-847页

作者： Singh, Omendra Kumar Panwar, N. L. GGS Indraprastha Univ Indira Gandhi Inst Technol Dept Mech & Automat Engn Delhi 110006 India Maharana Pratap Univ Agr & Technol Coll Technol & Engn Dept Renewable Energy Sources Udaipur 313001 Rajasthan India

The efficiency of energy collection of a flat plate type of solar air heater is low because of the large thermal losses and low heat transfer coefficient between the absorber plate and the air flowing in the duct. Packed beds have been successfully employed for the enhancement of the heat transfer coefficients in solar air heaters and such air heaters can be used for drying agricultural produce and space heating as well. This article deals with the theoretical investigation on the effects of thermal conductivity of material and geometry of a screen on the temperature variation in woven wire screen packed bed solar air heater. Theoretical results have been compared with the experimental results reported earlier by other researchers and found to match reasonably well with them. It has been found that the thermal performance depends upon a little on the thermal conductivity of screen material. Instead, it depends more on the geometry and an extinction coefficients of the matrix. A low value of extinction coefficient is desirable for maximum absorption of solar radiations and minimum thermal losses. The numerical method of analysis used here is based on finite difference approximation. The finite difference equations have been solved through a computer program in C++.

关键词： Packed bed solar air heater Thermal conductivity Extinction coefficient Screen geometry finite difference approximation

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Numerical study of an evolutive model for magnetostrictive materials

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MATHEMATICS AND COMPUTERS IN SIMULATION 2008年第1期77卷 22-33页

作者： Cerimele, M. M. Pistella, F. Valente, V. Ist Applicaz Calcolo M Picone I-00161 Rome Italy

A finite difference approximation method for the numerical study of the evolution equations for magnetoelastic materials is proposed and results concerning the numerical stability are established. Experiments on a specific test problem are carried out mainly to investigate on some evolutive phenomena such as the development and propagation of singular solutions. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： nonlinear parabolic-hyperbolic systems finite difference approximation numerical stability simulation

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