SKIBA, Yuri N.; CRUZ-RODRIGUEZ, Roberto C.    FILATOV, Denis M.. Solution of advection-diffusion-reaction problems on a sphere: High-resolution numerical experiments. []. , 37, 53172.   02--2023. ISSN 0187-6236.  https://doi.org/10.20937/atm.53172.

The implicit and unconditionally stable numerical method proposed in Skiba (2015) is applied to solve 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.

: Advection-diffusion problems; temperature waves of nonlinear combustion; blow-up regimes of nonlinear combustion; Gray-Scott nonlinear chemical model.