Fluid Dynamics: Solving the 2D Navier–Stokes Equations

Ionut Danaila (), Pascal Joly (), Sidi Mahmoud Kaber () and Marie Postel ()
Additional contact information
Ionut Danaila: Laboratoire de Mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Laboratoire Jacques-Louis Lions
Marie Postel: Laboratoire Jacques-Louis Lions

Chapter Chapter 15 in An Introduction to Scientific Computing, 2023, pp 327-365 from Springer

Abstract: Abstract The Navier–Stokes system of partial differential equations (PDEs) contains the main conservation laws that universally describe the evolution of a fluid (liquid or gas). In this chapter, we describe step-by-step the implementation of a numerical methods solving this problem using second-order finite-difference schemes for the space discretization. Time-integration is based on a projection method using a combination of Adams–Bashforth and Crank–Nicolson schemes. This method implies several basic algorithms that could be used for other problems: Thomas algorithm for solving tridiagonal linear systems, ADI methods for the time-integration of Helmholtz-type problems, Fourier decomposition for periodic Poisson problems, etc. The performance of the method is illustrated by simulating simple, but very nice flows: Kelvin-Helmholtz instability, vortex evolution and vortex dipole interactions.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-35032-0_15

Ordering information: This item can be ordered from
http://www.springer.com/9783031350320

DOI: 10.1007/978-3-031-35032-0_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().