Title: On the Convergence of Discrete Approximations to the NavierStokes Equations Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 1330194721
ISBN 13: 9781330194720
Binding: PAP
Condition: New
Weight: 123 grams

About this title

Synopsis

Understanding how discrete approximations converge to the Navier–Stokes equations

Learn how finite-difference schemes can accurately model fluid flow by building a rigorous foundation for discrete operators and their properties. This work develops the math needed to prove convergence for periodic problems and shows how to handle the mix of initial value and boundary value conditions.

Two clear, focused chapters walk you through the setup, from discretizing time and space to defining the discrete operators that mimic gradient, divergence, and Laplacian. You’ll see how these operators interact, the role of orthogonal projections, and how to formulate a stable, implementable scheme. The author also discusses limitations and what is required to extend results to more complex boundary conditions.
What you’ll experience

Grounding in the discrete operators D, G, and P, and how they resemble their continuous counterparts
A step-by-step look at a multi-stage time-stepping scheme and its discrete pressure update
Theorems that establish decompositions and orthogonality, plus conditions that ensure uniqueness and stability
Convergence results in bothLp and maximum norms, including error estimates and norms used
Discussion of two- and three-dimensional cases, and the impact of boundary conditions and Reynolds number

Ideal for readers who want a rigorous, hands-on view of numerical analysis for fluid dynamics, especially those studying numerical methods for the Navier–Stokes equations and related quasi-linear systems.

Whether you are a graduate student, researcher, or professional who needs a solid mathematical foundation for computational fluid dynamics, this edition provides detailed proofs and careful construction of the discrete framework needed for reliable simulations.

Ideal for readers of advanced applied mathematics and numerical analysis texts on fluid mechanics.

"About this title" may belong to another edition of this title.

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