High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids

The transport process is an important part of the research fluid dynamics, especially when it comes to tracer advection in atmosphere or ocean dynamics. In this paper, a series high-order semi-Lagrangian methods for on sphere are considered. formulated entirely three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate systems. underlying idea method find value field/tracer at departure point through interpolating values its surrounding grid points point. implementation divided into following two main procedures: finding by integrating characteristic equation backward and then interpolate first procedure, three utilized solve locations points, including commonly used midpoint-rule explicit Runge–Kutta (RK) methods. second one, interpolation, four new presented, (1) linear interpolation; (2) polynomial fitting based least square method; (3) global radial basis function stencils (RBFs), (4) local RBFs. For latter interpolation methods, we that crucial select optimal shape parameter function. A Gauss hill case compare contrast terms their accuracy, conservation properties. addition, proposed applied standard test cases, which include solid body rotation, shear deformation twin slotted cylinders, evolution moving vortex. It demonstrates could simulate all cases reasonable accuracy efficiency.