User Forum of Software BASEMENT

sajjad

User

Registered: 2014-10-01

Posts: 101

Discretization in Basement

Is the scheme used in Basement is well-balanced (preserves stationary states) ? The space discretisation is 1d or 2d?

Christian Volz

User

Registered: 2014-09-04

Posts: 31

Re: Discretization in Basement

Hello Sajjad

yes, the scheme used in BASEMENT is well-balanced. Simulating standing water over an irregular topography should not result in fluxes or velocities. You may perhaps encounter some minor velocities at the dry-wet interfaces, which are difficult to treat properly. (Actually, we also encountered a small bug in the current release if the tag "dynamic_depth_solver" is activated. In such scenarios the well-balancing may be violated in some scenarios. This bug should be fixed in the next release).

The term "space discretisation" means the discretization of the topography? In my point of view, the topography is discretized with second order accuracy. We allow for linearly varying bed levels within the cells (second order accuracy), in contrast to schemes with constant bed levels within the cells (first order accuracy).

Regards,
Christian

sajjad

User

Registered: 2014-10-01

Posts: 101

Re: Discretization in Basement

Thank you for your kind reply. By space discretisation , I mean to say the discretisation of the solution (unit discharges in x & y dir. and depth of flow). The values of these variables are determined at cell-centres or at nodes by the model but we need flux values at the edge's centre for Riemann pb formulation. So we need to interpolate for the solution variables at the intercell boundary. This interpolation can be zero-order, ist order, second order or even higher schemes. Which order schemes basement makes use of? Regards

Christian Volz

User

Registered: 2014-09-04

Posts: 31

Re: Discretization in Basement

In BASEMENT we assume a constant water elevation within the cell for the reconstruction of the water levels at the cell edges. This corresponds to a first order accurate scheme. (However, as I have said before, the topography is linearly varying within the cell, which corresponds rather to a second-order accurate representation of the topography).