Solution of advection-diffusion-reaction problems on a sphere: high-resolution numerical experiments

Abstract

The implicit and unconditionally stable numerical method proposed in Skiba (2015) is applied for solving linear advection-diffusion-reaction problems and nonlinear diffusion-reaction problems on a sphere. Numerical experiments carried out on a high-resolution spherical mesh show the effectiveness of the method in modelling linear advection-diffusion processes on a sphere (dispersion of pollution in the atmosphere), and nonlinear diffusion processes (propagation of nonlinear temperature waves, blow-up regimes of combustion, and chemical reactions in the Gray-Scott model). The method correctly describes the mass balance of a substance in forced and dissipative systems, and conserves the total mass and norm of the solution in the absence of forcing and dissipation.