The "UNSTEADY_NAVIER_STOKES" script solves the 2D steady Navier-Stokes equations.
The space discretization is performed by means of the standard Galerkin approach.
Bilinear quadrangular elements are used for the pressure and biquadratic quadrangular elements are used for the velocity.
This pressure and velocity interpolation satisfies the so-called LBB condition, which ensures the solvability of the algebraic system.
For the time integration the theta-method has been implemented. According to the value of theta these schemes are obtained:
0 -> Forward Euler
1/2 -> Crank-Nicolson
3/4 -> Galerkin
1 -> Backward Euler
The FEM parameters such as the number of finite elements and the number of Gauss integration points can be easily chosen.
The functions and the examples are developed according with Chapter 6 "Viscous incompressible flows" of the book "Finite Element Methods for flow problems" of Jean Donea and Antonio Huerta.
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Andrea La Spina (2020). 2D Unsteady Navier-Stokes (https://www.mathworks.com/matlabcentral/fileexchange/60869-2d-unsteady-navier-stokes), MATLAB Central File Exchange. Retrieved .