A Contemporary Scheme for Semi-Lagrangian Advection

Henry Juang


The semi-Lagrangian advection method is not new. We all know the most advantage of using a semi-Lagrangian method for advection is to avoid the numerical instability due to nonlinear computation of Eulerian method, thus we can have a large time step while using semi-Lagrangian advection method. For more than two decades, the concept of semi-Lagrangian advection for efficient computation has been applied to atmospheric and oceanic modeling with different numerical methods of implementation. Those methods were concentrated on the determination of trajectory, the accuracy of the interpolation, the time integration with semi-implicit, the remap of polar area for global modeling, the treatment of orographic resonant etc etc, and it comes to be more on the mass conservation and high order interpolation with monotonic and positive definiteness for up to date consideration, I called it contemporary schemes while the semi-Lagrangian considers mass conservation integration and/or interpolation. In this seminar, I would like to introduce a contemporary semi-Lagrangian advection scheme. It is contemporary because the method has the same consideration of mass conserving, and it is not 'very' traditional. The method has no need to do iteration to determine trajectory, no need to do interpolation for the Lagrangian forcing, no need to remap the polar area, and no need to treat orographic resonant. For massively parallel computing, it has no need to generate halo but using transpose to make sure global mass conservation interpolation by dimensional split in 3D advection. It is called non-iteration dimensional-split semi-Lagrangian (NDSL) method. Several theoretical test results and implementation into GFS will be presented.