Amik St-Cyr
NCAR-UCAR
vendredi 4 mars 11h00
The primitive equations are ill posed with any specification of
local point wise boundary conditions. This represents a major set
back for adaptive mesh refinements. They hold the promise of
high-resolution at a lower computational cost if the time step can still
be made efficient for climate modeling. The purpose of this work is
to explore an alternative to the traditional interpolation based
semi-Lagrangian time integrators employed in atmospheric models.
A novel aspect of the present study is that operator splitting is applied
to a purely hyperbolic problem rather than the incompressible Navier-Stokes
equations. The underlying theory of operator integration factor splitting is
reviewed and the equivalence with semi-Lagrangian schemes is
established. A nonlinear variant of integration factor splitting
is proposed where the advection operator is expressed in terms of
the relative vorticity and kinetic energy. To preserve stability,
a fourth order Runge-Kutta scheme is applied for sub-stepping.
An analysis of splitting errors reveals that OIFS is compatible with the
order conditions for linear multi-step methods. The new scheme is
implemented in a spectral element shallow water model using an
implicit second order backward differentiation formula for Coriolis and gravity
wave terms. Numerical results for standard test problems demonstrate
that much larger time steps are possible leading to greatly improved
performances.