Application of Splitting Algorithm for Solving Advection-Diffusion Equation on a Sphere
The new algorithm proposed in Skiba (Int. J. Numer. Methods Fluids (2015), https://doi.org/10.1002/fld.4016) is applied for solving linear and nonlinear advection-diffusion problems on the surface of a sphere. The discretization of advection-diffusion equation is based on the use of a spherical grid, finite volume method and the splitting of the operator in coordinate directions. The numerical algorithm is of second order approximation in space and time. It is implicit, unconditionally stable, direct (without iterations) and rapid in realization. The theoretical results obtained in Skiba (Int. J. Numer. Methods Fluids (2015), https://doi.org/10.1002/fld.4016) are confirmed numerically by simulating various linear and nonlinear advection-diffusion processes. The results show high accuracy and efficiency of the method that correctly describes the advection-diffusion processes and balance of mass of substance in the forced and dissipative discrete system, and conserves the total mass and L2-norm of the solution in the absence of external forcing and dissipation.
The work was partially supported by the grant No. 14539 of the National System of Researchers of Mexico (SNI, CONACyT) and scholarship of CONACyT, Mexico.