Examples
All benchmarks, examples and applications cases to be run by Kratos. Note that unit tests are in Kratos repository and NOT here
Space and time convergence tests
Author: Riccardo Tosi
Kratos version: 9.0
Source files: section 2.7 of [1]
Space convergence
We solve the transient convection diffusion equation
and validate its reference implementation. We refer to section 2.7.1 of [1] for details.
We validate the implementation by computing the norm of the error as
, where
is the mesh size,
and
are the analytic and FEM solutions, respectively.
<img src="convergence_error_convection_diffusion_explicit_solution.jpg"alt="velocity" style="width: 500px;"/>
The figure shows that the error converges as expected for both quasi-static ASGS and quasi-static OSS.
Time convergence
We solve the transient convection diffusion equation
and validate its reference implementation. We refer to section 2.7.2 of [1] for details.
The analytic solution at time is
. Therefore, it is possible to compute the
norm of the error as
, where
is the mesh size,
and
are the analytic and FEM solutions, respectively. It is expected to obtain an order four accuracy for the Runge-Kutta 4 time integration scheme.
<img src="convergence_error_time_convection_diffusion_bar.jpg"alt="velocity" style="width: 500px;"/>
The figure shows that the time accuracy is of order four, as expected.
References
[1] Tosi, R. (2020). Eulerian convection diffusion explicit elements (p. 27). p. 27. Retrieved from https://github.com/KratosMultiphysics/Documentation/blob/master/Resources_files/convection_diffusion_explicit_elements/Eulerian_convection_diffusion_explicit_element.pdf