Perturbation Methods in Applied Mathematics |
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12 pages matching potential flow in this book
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Introduction | 1 |
Twovariable expansion procedures | 79 |
Applications to partial differential equations | 120 |
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A₁ A₁(x a² Fo amplitude approximate equations asymptotic expansion at² B₁ behavior boundary condition Equation boundary conditions boundary layer boundary-layer equations C₁ characteristic coefficients consider const constant constructed coordinates corresponding curl differential equations dimensionless dominant dr² dx² equation Equation exact solution example expansion Equation expansion procedure expansion valid exponential exponential decay F₁ Figure fixed flow functions h₁ initial conditions inner expansion intermediate limit limit process linear matching Navier-Stokes equations nonlinear ordinary differential equations oscillations outer expansion outer solution partial differential equations periodic solution perturbation phase plane potential flow result satisfy Section shock waves side of Equation singular solution of Equation subcharacteristic surface theory transonic two-variable u₁ uniformly valid upstream infinity variables velocity viscous zero ди ду дх