alsgregory / quasi_geostrophic_model Goto Github PK

Add the following tests:

• Test the MinDx feature.

• Test the noise convergence (of the mean or a statistic)

• Insert FunctionSpace to be Argument level in quasi_geostrophic and remove Mesh from this list of Arguments. Would allow Functions in tests / demos to just simply be assigned on to one another as they can come from same FunctionSpace.

Allow the variance argument in the quasi_geostrophic model to be removed and replaced by an OU process, which IT'S variance is then given in place of the variance argument, allow this to be correlated (easily, as it's just scalar OU) between pairs of two-level simulations.

Create a random infinite dimensional initial condition for the QG model in way that was discussed in meeting:

Solve one time-step, with random forcing (additive to q to find psi), and use that as new initial condition.

• Find out how to correlate the noise input into the system: Using helmholtz solution, and then can inject / prolong this

Allow an argument to be entered to correlate the noise input to another system (a coarse / fine version) so that it can be prescribed at every time-step
Update on how to do this:

• Be able to choose whether it is one level or two model. And then the length of tuples of solvers etc will be d. Best way to do this is provide a tuple of FunctionSpaces, or just one FunctionSpace and deduce from this.
• Takes function spaces which belong to meshes on at least a hierarchy of two levels.
• Change class details, such as name and args to match two-level-qg-model
• Put all solvers / solver functions needed for both coarse and fine solve etc in tuples length d, then access like that.
• Then construct a fine and a coarse solution side-by-side and use same noise / helmholtz solution. (Do 2 x fine u_ helmholtz solution sums, and then use this for input for projection for coarse self.forcing).
• Make sure we check if the adapted time-step is exactly half on fine, as it should have to be due to refined mesh.
• Thus think about what to do when the time-step is cut in half by end-time (check for fine time-step and if not cut both fine and coarse, if one fine time-step is allowed through but not second -> just add on the scaled / with smaller than usual fine time-step / u_ solution to first fine u_ solution to make up coarse)
• Changes tests / demos and also construct two-level tests

Adjust two_level_quasi_geostrophic so that any MeshHierarchy.refinements_per_level can be used

• Check and alter the time-step used in the solve for q in the initial condition (with random psi).

Make sure that the system is not being propagated forward different time-steps at the start (I.C.) for different resolutions. Try doing a standard time-step, say 1.0. (By altering self.qg_class.const_dt - like what is done for coarse on two-level) Then all resolutions should be solved once for same time.