Journal of Scientific Computing
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
SIAM Journal on Numerical Analysis
The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
Journal of Computational Physics
Stable and unstable formulations of the convection operator in spectral element simulations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations
Journal of Scientific Computing
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows
Journal of Scientific Computing
Journal of Computational Physics
Nonlinear OIFS for a hybrid galerkin atmospheric model
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
Hi-index | 0.00 |
The purpose of this paper 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.