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Atmósfera
versão impressa ISSN 0187-6236
Resumo
SKIBA, Yuri N.; CRUZ-RODRIGUEZ, Roberto C. e FILATOV, Denis M.. Solution of advection-diffusion-reaction problems on a sphere: High-resolution numerical experiments. Atmósfera [online]. 2023, vol.37, 53172. Epub 02-Maio-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.
Palavras-chave : Advection-diffusion problems; temperature waves of nonlinear combustion; blow-up regimes of nonlinear combustion; Gray-Scott nonlinear chemical model.