E. V. Vorozhtsov, N. N. Yanenko

Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems

• Broschiertes Buch

Produktbeschreibung

As a result of the numerical simulation of multidimensional gas dynamics problems on a computer, the output information is obtained in the form of immense arrays of numerical data. In this connection, there arises the problem of extracting the actually needed information from these arrays; in other words, it is necessary to solve the problem of information compression. In particular, the numerical solution of gas dynamics problems often aims at the information on the solution singularities-the shock waves, contact interfaces, slip lines, etc. Our book is devoted to the development and investigation of accuracy of the algorithms for the localization of such singularities. In addi tion, the questions of development of the algorithms for the classification of singularities into several types (on the basis of shock-capturing numerical solutions of two-dimensional gas dynamics problems) are considered for the first time in the monographic literature. For this purpose, some ideas and methods of the modern theory of digital-image processing and of the pattern recognition theory are used. The information obtained at the output of the systems of the singularities classification presented in this book is rich in content, because it contains both physical and geometrical characteristics of recognized objects. Therefore, such "intellectual" systems of information ex traction may be used in the expert systems of automated design of aero dynamic bodies which meet some optimality requirements. This is, in our opinion, very attractive from the point of view of applications.

Produktdetails

• Scientific Computation
• Verlag: Springer, Berlin
• Softcover reprint of the original 1st edition 1990
• Seitenzahl: 420
• Erscheinungstermin: 19. September 2011
• Englisch
• Abmessung: 235mm x 155mm x 23mm
• Gewicht: 632g
• ISBN-13: 9783642647703
• ISBN-10: 3642647707
• Artikelnr.: 36115610

Inhaltsangabe

1. Introduction and Necessary Notions from the Theory of Difference Schemes for Gas Dynamics Problems.- 1.1. Original Equations. Jump Conditions in the Case of One-Dimensional Gas Flow.- 1.2. Jump Conditions in the Case of Two-Dimensional Gas Flow.- 1.3. Homogeneous Difference Schemes and Their Differential Approximations.- 1.4. On the Applicability of Progressive Wave-Type Solutions of the First Differential Approximation Equations.- 2. Differential Analyzers of Shock Waves in One-Dimensional Gas Flows.- 2.1. An Introductory Example.- 2.2. Existence and Uniqueness of the Smeared Wave Center in the Solution of the System with Artificial Viscosity.- 2.3. Scheme Viscosity and Smeared Shock Wave Center Existence.- 2.4. An Analysis of Difference Schemes of Gas Dynamics.- 2.5. The Application of Differential Analyzers in Problems of Shock Wave Formation.- 3. Differential Analyzers of Shock Waves in Two-Dimensional Gas Dynamic Computations.- 3.1. Method for Investigating the Properties of Curvilinear Shock Front "Smearing".- 3.2. Localization of the Smeared Shock Wave Center in the Case of a Straight Front.- 3.3. Shock Localization by Moving Grids.- 3.4. Computational Examples.- 4. Differential Analyzers of Contact Discontinuities in One-Dimensional Gas Flows.- 4.1. Methods for the Localization of Contact Discontinuities in the Presence of K-Consistence.- 4.2. K-Consistence Property of the First Differential Approximation in the Two-Dimensional Case.- 4.3. Methods of K-Inconsistence Suppression.- 4.4. The Contact Residual Subtraction Method.- 4.5. Computational Examples.- 5. Optimization Techniques of the Discontinuities Localization.- 5.1. An Analysis of the Miranker-Pironneau Method.- 5.2. Incorporation of the Information on Approximation Viscosity into the BasicFunctional.- 5.3. Shock Localization on the Basis of Function Minimization.- 5.4. Gradient Methods of Basic Functional Minimization.- 5.5. Computational Examples.- 5.6. On Optimization Algorithms for the Localization of Contact Discontinuities.- 5.7. An Optimization Method for the Localization of Weak Discontinuities.- 5.8. A Generalization of the Miranker-Pironneau Method for the Case of Polar Coordinates in a Filtration Problem.- 6. Difference Solution Refinement in the Neighborhood of Strong Discontinuities.- 6.1. Construction of the Basic Functional.- 6.2. Solution Refinement on the Basis of the Least-Squares Method.- 6.3. On the Difference Solution Refinement in the Neighborhood of a Shock Wave Front.- 6.4. Computational Examples.- 7. Classification of Singularities in Gas Flows as the Pattern Recognition Problem.- 7.1. Methodologies of Pattern Recognition.- 7.2. Image Formation.- 7.3. Image Segmentation.- 7.4. Feature Space.- 7.5. Algorithms of Pattern Classification.- 7.6. Examples of Pattern Classification in the Numerical Solutions of Two-Dimensional Gas Dynamics Problems.- Concluding Remarks.- References.