Abstract
A fully implicit (FI) time integration method has been implemented into a
spectral finite element shallow water equation model on a sphere, and it is
compared to existing fully explicit leapfrog and semi-implicit methods for a
suite of test cases. This experiment is designed to determine the time step
sizes that minimize simulation time while maintaining sufficient accuracy for
these problems. For test cases without an analytical solution from which to
compare, it is demonstrated that time step sizes 30 to 60 times larger than
the gravity wave stability limits and 6 to 20 times larger than the advective
scale stability limits are possible using the FI method without a loss in
accuracy, depending on the problem being solved. For a steady-state test case,
the FI method produces error within machine accuracy limits as with existing
methods, but using an arbitrarily large time step size.
