Trajectory-Tracking Scheme in Lagrangian Form for Solving Linear Advection Problems: Interface Spatial Discretization

Abstract

Abstract A previous Lagrangian linear advection scheme (trajectory-tracking scheme) is modified to achieve local mass conservation in this paper, which is more favorable to climate modeling. The discretized tracer parcels are volumes with interfaces instead of centroids. In 2D problems, the parcels are polygons and the interfaces are described by polygonal edges with a finite number. Because polygons will deform under the background wind field, a curvature-guard algorithm (CGA) is devised to retain accurate representation of the deformed interfaces among parcels. The tracer mass carried by parcels is mapped onto the regular latitude–longitude mesh by a first-order conservative remapping algorithm that can handle concave polygons. Several standard test cases have been carried out to show the effectiveness of the new scheme.