Implementation of Finite Element Methods for Navier-Stokes Equations
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numeric...
Main Author: | |
---|---|
Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1981, 1981
|
Edition: | 1st ed. 1981 |
Series: | Scientific Computation
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Notations
- 1. Elliptic Equations of Order 2: Some Standard Finite Element Methods
- 1.1. A 1-Dimensional Model Problem: The Basic Notions
- 1.2. A 2-Dimensional Problem
- 1.3. The Finite Element Equations
- 1.4. Standard Examples of Finite Element Methods
- 1.5. Mixed Formulation and Mixed Finite Element Methods for Elliptic Equations
- 2. Upwind Finite Element Schemes
- 2.1. Upwind Finite Differences
- 2.2. Modified Weighted Residual (MWR)
- 2.3. Reduced Integration of the Advection Term
- 2.4. Computation of Directional Derivatives at the Nodes
- 2.5. Discontinuous Finite Elements and Mixed Interpolation
- 2.6. The Method of Characteristics in Finite Elements
- 2.7. Peturbation of the Advective Term: Bredif (1980)
- 2.8. Some Numerical Tests and Further Comments
- 3. Numerical Solution of Stokes Equations
- 3.1. Introduction
- 3.2. Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure
- 3.3. Velocity—Pressure Formulations: Continuous Approximation of the Pressure and Velocity
- 3.4. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity
- 3.5. Vorticity Stream-Function Formulation: Decompositions of the Biharmonic Problem
- 4. Navier-Stokes Equations: Accuracy Assessments and Numerical Results
- 4.1. Remarks on the Formulation
- 4.2. A review of the Different Methods
- 4.3. Some Numerical Tests
- 5. Computational Problems and Bookkeeping
- 5.1. Mesh Generation
- 5.2. Solution of the Nonlinear Problems
- 5.3. Iterative and Direct Solvers of Linear Equations
- Appendix 2. Numerical Illustration
- Three Dimensional Case
- References