Diffusion of Hill#
This directory contains two benchmarks of a 2D hill diffusing away over time. In the first benchmark, 1_sine_zero_flux.prm, the left and right boundary condition for diffusion is zero flux, so the topography of the left and right mesh corner point increases over time, while the maximum height of the hill decreases. The second benchmark, 2_sine_const_h.prm, fixes the topography at the left and right boundary. Note that in both cases we do not solve for velocity or temperature and only the mesh is deforming.
The postprocessor analytical_topography.cc should be compiled
with cmake and make using the provided CMakeLists:
$cmake -D Aspect_DIR=path/to/aspect/build/dir/ .
$make
This postprocessor outputs the topography
of the ASPECT mesh, as well as what the topography should be
according to the analytical solution. To run the benchmarks:
$./aspect 1_sine_zero_flux.prm
The topography and analytical solution can be plotted with gnuplot using the provided scripts:
$gnuplot plot_topo_error_benchmark_2.gnuplot
$gnuplot plot_topo_error_benchmark_1.gnuplot
$gnuplot plot_topo_benchmark_2.gnuplot
$gnuplot plot_topo_benchmark_1.gnuplot
of which the first 2 plot the percentage error between the topography and analytical solution, and the last two the actual values.
When playing with the parameters of the input file, you will notice a dependence of the error on timestep and mesh resolution.