Method of Discrete VorticesCRC Press, 31 gru 1992 - 464 Method of Discrete Vortices presents a mathematical substantiation and in-depth description of numerical methods for solving singular integral equations with one-dimensional and multiple Cauchy integrals. The book also presents the fundamentals of the theory of singular equations and numerical methods as applied to solving problems in such branches of mechanics as aerodynamics, elasticity, and electrodynamics. |
Spis treści
An Introduction to Singular Integral Equations in Aerodynamics | 1 |
Introduction | 21 |
Quadrature Formulas of the Method of Discrete Vortices | 29 |
Interpolation Quadrature Formulas for OneDimensional | 61 |
Quadrature Formulas for Multiple and Multidimensional | 75 |
Integral for a FiniteSpan Wing | 96 |
PoincaréBertrand Formula | 115 |
Equation of the First Kind on a Segment andor | 127 |
TwoDimensional Problems for Airfoils | 259 |
ThreeDimensional Problems | 283 |
Unsteady Linear and Nonlinear Problems | 303 |
Aerodynamic Problems for Blunt Bodies | 323 |
Some Questions of Regularization in the Method | 343 |
Singular Integral Equations of the Theory | 361 |
Moving Punches into an Elastic Strip | 380 |
Numerical Method of Discrete Singularities in Boundary | 387 |
Equations of the First Kind on a Circle Containing | 175 |
Singular Integral Equations of the Second Kind | 191 |
Singular Integral Equations with Multiple Cauchy | 217 |
Formulation of Aerodynamic Problems | 245 |
Reduction of Some Boundary Value Problems | 419 |
Conclusion | 425 |
| 433 | |
Kluczowe wyrazy i wyrażenia
A₁ aerodynamics airfoil axis B₁ belongs Belotserkovsky C₁ calculated canonic division Cauchy principal value characteristic equation circle class H coefficients consider contour corresponding denote discrete vortices dt¹ dt² dual equation E₁ equal f(to f(toj FIGURE flow past flow velocity following theorem form a canonic Fourier series Fredholm equation grid points h₁ Helmholtz equation Hence Inequality infinity k₁ kernel L₁ Laplace equation latter Lifanov linear algebraic equations method of discrete Muskhelishvili 1952 n₁ Neumann problem Note numerical method numerical solution piecewise smooth plane point Mo point q polynomial problem quadrature formulas reference points respect right-hand side second kind singular integral equation solution to Equation solving surface system of linear t-to t₁ Theorem trigonometric polynomial unique solution valid values variable vortex sheet x₁ Ζο ΣΣ