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Belotserkovsky S.M., Lifanov I.K. — Method of Discrete Vortices
Belotserkovsky S.M., Lifanov I.K. — Method of Discrete Vortices



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Название: Method of Discrete Vortices

Авторы: Belotserkovsky S.M., Lifanov I.K.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1993

Количество страниц: 451

Добавлена в каталог: 09.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Fredholm equations of second kind      181
Fredholm equations,elasticity theory and      362 -363
Fredholm equations,integrodifferential equations and      239
Fredholm equations,segments and      154
Fredholm’s theory of constructing      155
Free vortices      247
Free vortices,blunt body aerodynamics and      340
Free vortices,circulation of      304
Free vortices,discrete      304
Free vortices,jumping across airfoil surface by      358
Free vortices,strengths of      304
Free vortices,velocity of      318
Friction      14
Gamma functions theory      132
Gases,density of      7
Gases,dynamics of      8
Gases,energy dissipation of      8
Gases,flow of      7
Gases,moving in      8
Gases,pressure of      7
Gases,unperturbed flow of      7
Gases,unperturbed speed of      9
Gases,velocity of      7
Gaussian quadrature formulas      410
Generalized functions theory      374
Generalized polynomials      208
Grid points      21
Grid points,equally spaced      112
Grid points,unequally spaced      113
Grids      23
Hadamard criterion      146
Hadamard finite value      24
Harmonic function      327
Heat conduction law      370
Heat conductivity      371
Heat generation      370
Helmholtz equation      388
Helmholtz equation,Dirichlet and Neumann problems for      404—414
Helmholtz equation,Dirichlet and Neumann problems for,formulation of      404—408
Helmholtz equation,Dirichlet and Neumann problems for,model problems in      408—411
Hilbert’s kernel      4
Hilbert’s kernel,boundary value problems and      422
Hilbert’s kernel,elasticity theory and      363
Hilbert’s kernel,equations on circles with      182—190
Hilbert’s kernel,singular integral equations with      199—203
Hilbert’s kernel,singular integral equations with,of first kind      422
Hilbert’s kernel,singular integral equations with,variable coefficients and      212—215
Hilbert’s kernel,singular integrals over circles with      345
Hilbert’s kernel,singular integrals with      57—58
Hilbert’s Problem      4
Hilbert’s transform      397
History of singular integral equations      2—7
Holder conditions      30
Holder functions      208
Holder-continuous functions      398
Horseshoe vortices,blunt body aerodynamics and      323
Horseshoe vortices,discrete      284
Horseshoe vortices,oblique      249
Horseshoe vortices,slanting      293
Horseshoe vortices,straight      255
Horseshoe vortices,usual      254
Hydrodynamics      6
Improper integral      2
Incompressible fluids      14
Inertia      see "Virtual inertia"
Infinite discontinuities      343
Infinite-span vortex filament      249
Infinite-span wings      160
Influence functions      374
Integrable singularities      6
Integral equations      see "Singular integral equations"
Integrals      10
Integrals,Abel      309
Integrals,Bernoulli      14
Integrals,Cauchy      see "Cauchy integrals"
Integrals,Cauchy principal value of      3
Integrals,Cauchy — Lagrange      247
Integrals,divergent improper      2
Integrals,improper      2
Integrals,invariant      14
Integrals,multiple Cauchy      see "Multiple singular Cauchy integrals"
Integrals,singular      see "Singular integrals"
Integrals,two-dimensional      24
Integrodifferential equations      239—241
Integrodifferential equations in blunt body aerodynamics      324—327
Integrodifferential equations,Prandtl      58
Integrodifferential equations,two-dimensional      239
Internal point of the frame      75
Interpolation polynomial      399
Invariant integral      14
Inversion formulas      224
Inviscid compressible gas      7
Inviscid incompressible fluid      245
Irrotational flow      7
Iterated kernels      157
Jacobi polynomials      194
Jacobian      89
Jet hydrodynamics      6
Jordan’s two-dimensional measure      104
Joukowski airfoils      13
Joukowski theorem      247
Karman vortex street      430
Kernels,Cauchy      4
Kernels,continuous      155
Kernels,Hilbert’s      see "Hilberl’s kernel"
Kernels,iterated      157
Kinematic viscosity      15
Kolosov — Muskhelishvili formulas      361
Korneichuk inequality      70
Lame equations      372
Laplace equation      246
Laplace equation in boundary value problems      388
Laplace equation,Dirichlet and Neumann problems for      421—423
Leading edge      13
Leading edge of canonic trapezoids      299
Leading edge of trapezoids      296
Leading edge,equations for      300
Leading edge,two-dimensional airfoil problems and      260
Left-hand direct product      233
Lift      8
Lift of thin airfoils      1
Lift,coefficients of      15
Lift,maximum      8
Lift-generating structural elements      7
Lifting surface      21
Linear multipliers      194
Linear steady problems of aerodynamics      25
Linear unsteady problems      303—309
lines      29
Liouville theorem      6
Local flow velocity      342
Local shock waves      15
Local sound speed      9
Local supersonic zone      14
Locally polytropic processes      8
Logarithmic singularities      419 421
Lord Kelvin condition      337
Lyapunov contour      38
Lyapunov curves      24
Lyapunov curves,closed      39
Lyapunov curves,elasticity theory and      363
Lyapunov curves,nonintersecting      39
Lyapunov curves,open      51
Lyapunov curves,piecewise      52
Lyapunov curves,unclosed      51
Mach number      9
Mapping      18
Mass conservation law      8
Mass ejection      10
Maximum flight speed      15
Maximum lift      8
Maxwell equations      415
Meixner conditions      405
Metric of the space of functions      211
Minimum drag      8
Modified Bessel equation      391
Momentum conservation      8
Multi-dimensional singular integrals      24
Multi-dimensional singular integrals,quadrature formulas for      103—110
Multiple singular Cauchy integrals      24
Multiple singular Cauchy integrals on products of plane curves      224
Multiple singular Cauchy integrals,analytical solutions to      217—224
Multiple singular Cauchy integrals,defined      32
Multiple singular Cauchy integrals,integrodifferential equations and      239— 241
Multiple singular Cauchy integrals,inversion formulas for      224
Multiple singular Cauchy integrals,numerical solutions for      224—239
Multiple singular Cauchy integrals,numerical solutions for,canonic division and      229
Multiple singular Cauchy integrals,numerical solutions for,common multipliers and      227
Multiple singular Cauchy integrals,numerical solutions for,Cramer rule and      226
Multiple singular Cauchy integrals,numerical solutions for,uniform grids and      233
Multiple singular Cauchy integrals,numerical solutions for,unit-radius circles and      224
Multiple singular Cauchy integrals,of second kind      234
Multiple singular Cauchy integrals,one-dimensional      82
Multiple singular Cauchy integrals,Poincare — Bertrand formula and      120—124
Multiple singular Cauchy integrals,quadrature formulas and      75—83
Multiple singular integrals      24
Multiple singular integrals for finite-span wings      96—103
Multiple singular integrals in aerodynamics      83—92
Multiple singular integrals,Cauchy      see "Multiple singular Cauchy integrals"
Multiple singular integrals,quadrature formulas for      92—95
Multipliers      83
Muskhelishvili equations      363
n-dimensional torus      80
Natural regularizing factors      345
Neumann problem      412—417 also
No-circulation flow      261
No-penetration boundary conditions      259
No-penetration condition      245
No-penetration condition,blunt body aerodynamics and      324
No-penetration condition,three-dimensional airfoil problems and      284
No-penetration condition,two-dimensional airfoil problems and      279
No-penetration condition,wake      320
No-slip condition      245
Node of curves      32
Node vicinity      53
Noncirculatory flow      22
Noncirculatory flow,blunt body aerodynamics and      338
Noncirculatory flow,three-dimensional airfoil problems and      298
Nonintersecting Lyapunov curves      39
Nonintersecting segments      56
Nonintersecting smooth closed curves      217
Nonlinear unsteady problems      316—322
Nonpenetration condition      11
Nonsingular nodes      204
Nonzero total circulation      22
Numerical integration      see "Quadrature"
Oblique horseshoe vortices      249
One-dimensional Cauchy integrals      102
One-dimensional singular integrals      29 60
One-dimensional singular integrals of first kind      217
One-dimensional singular integrals on circles      66—69
One-dimensional singular integrals on segments      39—51
One-dimensional singular integrals on segments,theorems for      42— 48
One-dimensional singular integrals over closed contours      32—39
One-dimensional singular integrals over piecewise smooth curves      51—56
One-dimensional singular integrals with Hilbert’s kernel      57—58
One-dimensional singular integrals,Cauchy      77
One-dimensional singular integrals,defined      29—32
One-dimensional singular integrals,Poincare — Bertrand formula and      115—120
One-dimensional singular integrals,theory of      29—32
Open curves      51
Optimal airfoil      1
Optimal flight speed      15
Oscillating wings      288
Outer force      7
Parachutes      281
Perfect incompressible fluid      83
Permeable airfoils      281—282
Perturbed flow      8
Piecewise Lyapunov curves      52
Piecewise smooth curves      30
Piecewise smooth curves,singular integral equations on      203 -211
Piecewise smooth curves,singular integrals over      51—56
Plane curves      224
Plane strain      361
Plane stress      361
Poincare — Bertrand formula      24 124
Poincare — Bertrand formula,full equation on segments and      157
Poincare — Bertrand formula,multiple singular Cauchy integrals and      120—124
Poincare — Bertrand formula,one-dimensional singular integrals and      115—120
Poincare — Bertrand formula,singular integral equations on segments and      136
Poincare — Bertrand formula,validity of      119
Poisson coefficient      385
POLYGONS      249
Polynomials      429
Polynomials,Chebyshev      24
Polynomials,generalized      208
Polynomials,interpolation      399
Polynomials,Jacobi      194
Polynomials,trigonometric      202
Polytropic processes      8
Potential      13
Power-law integrable discontinuities      426
Prandtl equation      58
Prandtl vortex      321
Pressure      15
Pressure,contact      369
Pressure,decrease in      379
Pressure,distribution of      341
Pressure,gas      7
Pressure,gas flow      8
Quadrangular-triangular vortices      330
Quadrature formulas      24
Quadrature formulas for multi-dimensional singular integrals      103—110
Quadrature formulas for multiple Cauchy integrals      75—83
Quadrature formulas for multiple singular integrals      92—95
Quadrature formulas for singular integrals for finite-span wings      96—103
Quadrature formulas for singular integrals in aerodynamics      83—92
Quadrature formulas for singular integrals on circles      66—69
Quadrature formulas for singular integrals on segments      39—51
Quadrature formulas for singular integrals over closed contours      32—39
Quadrature formulas for singular integrals over piecewise smooth curves      51—56
Quadrature formulas for singular integrals with Hilbert’s kernel      57—58
Quadrature formulas for singular integrals,estimation of      346
Quadrature formulas for singular integrals,multiple Cauchy integrals and      75—83
Quadrature formulas for singular integrals,theorems for      42—48
Quadrature formulas,coefficients of      429
Quadrature formulas,construction of      426
Quadrature formulas,Gaussian      410
Quadrature formulas,regularizing factors and      350
Quadrature formulas,theory of      29— 32
Quadrature formulas,unification of difference formulas and      58—60
Radiation      405
Rectangle rule formulas      180
Rectangles      54
Rectangular vortices      255
Rectangular wings,finite-span      239
Rectangular wings,flow with circulation past      283—288
Rectangular wings,flow without circulation past      288 -293
Rectilinear vortex segments      249
Reference points      21
Reference points,elasticity theory and      368
Reference points,three-dimensional airfoil problems and      284
Reference points,two-dimensional airfoil problems and      76
Reference points,velocity component at      304
Regularizing factors      135
Regularizing factors for singular integral equations      350—357
Regularizing factors in unsteady aerodynamic problems      357—358
Regularizing factors,natural      345
Regularizing factors,self-      345
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