We compare 4 numerical principles that have smoothing and/or time marching properties and show the similarities between them.
We model the dynamics of solar heating and of the heat ground flux. We can reconstruct why the peak of heat is in the afternoon and not at noon (when the sun is in the zenith).
We formulate the discretization of a heat flow model for an implicite finite volume method on an irregular grid and implement it for an 1-dimensional application. We give the detailled derivation from the partial differential equation to the FVM discretization and the implementation with vectorized Python code.