ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 5
Formulation of FEM for Unsteady Problems
Two alternatives for formulating time dependent problems are called coupled space-time
formulation and semi-discrete formulation. The first on
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 1
Governing Equations of Fluid Flow and Heat Transfer
Following fundamental laws can be used to derive governing differential equations that are solved in
a Computational Fluid Dynamics
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 7
Incompressible Flow Solutions
Incompressible flows are by far the most common type of flows encountered in engineering
problems. They are different than compressible flows mainly due
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 9
Least-Squares Finite Element Solution of Compressible Euler
Equations
There are a number of fundamental differences between the numerical solution of incompressible
and compressible f
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 6
Petrov-Galerkin Formulations for Advection Diffusion Equation
In this chapter well demonstrate the difficulties that arise when GFEM is used for advection
(convection) dominated probl
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 4
Computer Implementation for 1D and 2D Problems
In this chapter MATLAB codes for 1D and 2D problems are provided. Also a manual for 2D mesh generator is
given.
4.1 MATLAB Code for 1D F
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 2
Formulation of FEM for One-Dimensional Problems
2.1 One-Dimensional Model DE and a Typical Piecewise Continuous FE Solution
To demonstrate the basic principles of FEM let's use the fo
ME 582 Finite Element Analysis in Thermofluids
Dr. Cneyt Sert
Chapter 3
Formulation of FEM for Two-Dimensional Problems
3.1 Two-Dimensional FEM Formulation
Many details of 1D and 2D formulations are the same. To demonstrate how a 2D formulation works
well
METU Mechanical Engineering Department
ME 582 Finite Element Analysis in Thermofluids
Integration by Parts in 1D and 2D
Integration by Parts
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Gradient and Laplace Operators
Divergence Theorem
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Other Useful Forms
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