|
|
The first example consists in solving an homogeneous transient convection-diffusion equation
in (0,1) with initial condition
User can choose among three different time-integration schemes:
 |
Crank Nicolson, a second order classical integration method |
| |
R22, a fourth order method based on Padé approximations (2 stages) |
| |
R33, a sixth order method based on Padé approximations (3 stages) |
and five different spatial discretization techniques:
| |
Galerkin |
| |
Least-Squares |
| |
Streamline Upwind Petrov-Galerkin (SUPG) |
| |
Galerkin Least-Squares (GLS) |
| |
Sub-Grid Scales (SGS) |
If one of the stabilized formulations (SUPG, GLS, SGS) is used,
it is necessary to define a stabilization parameter. In this case,
we do not use a single coefficient but a matrix adapted to the
integration scheme.
Figures below show numerical solution at time t = 0.6 compared with the analytical one.
Solution has been computed using Galerkin method and three different time-integration schemes.
A mesh of 150 linear elements has been used in the computation, and time step
is chosen to have a Courant number C=4.
Note that solution improves when using a higher-order integration scheme.
|
|
Back to Unsteady Convection-Diffusion