Aec Computing and Applied Mathematics Center: Aec Research and Development Report (Classic Reprint) - Hardcover
Synopsis
Explore a practical approach to advanced fluid dynamics modeling.
This report introduces an implicit numerical scheme for solving a nonlinear, third-derivative extended version of the shallow water equations. It covers transforming equations to a dimensionless, characteristic-like form and developing a stable finite difference method that handles boundary and initial conditions carefully.
The discussion blends theory with hands-on computation. It shows how to convert complex equations into a computable scheme, manage stability near boundaries, and verify results through numerical experiments on a large IBM computer. You’ll see how the method tracks wave motion, handles discharge as a key variable, and limits artificial reflections at the channel ends. The work emphasizes the practical steps needed to obtain robust solutions without sacrificing physical realism.- Learn how to cast a mixed hyperbolic–third-derivative system into a tractable finite difference scheme.
- See how boundary conditions and conservation laws drive stable, implicit corrections.
- Understand how the discharge variable q is used to advance the solution in time and space.
- Review numerical results that illustrate wave propagation and spreading in a channel.
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