Matsuno-Gill Problem

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Below are three codes to solve the Matsuno-Gill problem, in the form posed by Gill (1980) in his 'simple solutions' paper, in Python or Matlab. All of these codes should run as is to produce an output of the standard Gill problem. The numerical codes can then easily be modified by the user for different source terms.

Sample PDF output of analytic solution For more plots, click here

Python code for analytic model. Calculates and plots the analytic solution

Matlab code for analytic model. Calculates and plots the analytic solution

Numerical Model 1. Timesteps the linear shallow water equations to a steady solution using a grid point model.

Numerical model 2. Obtains the solution to the steady problem by directly solving the steady linear shallow water equations. Uses FFTs in x direction and finite differencing in y. This code is more accurate than Numerical Model 1.