Numerical weather prediction in two dimensions with topography, using a finite volume method
For researchers in numerical weather prediction, this work offers an improved finite volume method for handling topography, though it is an incremental advance over existing schemes.
The paper develops a finite volume scheme for 2D inviscid primitive equations with topography, introducing a projection method to enforce boundary conditions. The scheme reduces errors near topography compared to standard methods, and numerical experiments show that random small-scale forcing leads to recurrent large-scale patterns in temperature and velocity fields.
We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system of equations. In that respect, a version of a projection method is introduced to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. The resulting scheme allows for a significant reduction of the errors near the topography when compared to more standard finite volume schemes. In the numerical simulations, we first present the associated good convergence results that are satisfied by the solutions simulated by our scheme when compared to particular analytic solutions. We then report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated. The numerical results show that such a forcing is responsible for recurrent large-scale patterns to emerge in the temperature and velocity fields.