Registro de resúmenes

Reunión Anual UGM 2022


MSG-3

 Resumen número: 0044  |  Resumen aceptado  
Presentación oral

Título:

SOLUTION OF ADVECTION-DIFFUSION-REACTION PROBLEMS ON A SPHERE USING A DIRECT, IMPLICIT AND UNCONDITIONALLY STABLE SPLITTING ALGORITHM

Autores:

1 Yuri N. Skiba ← Ponente
Instituto de Ciencias de la Atmósfera y Cambio Climático, Universidad Nacional Autónoma de México
skiba@unam.mx

2 Roberto C. Cruz-Rodríguez
Instituto de Ciencias de la Atmósfera y Cambio Climático, Universidad Nacional Autónoma de México
roberto.cruz.rdg@gmail.com

Sesión:

MSG Modelación de sistemas geofísicos Sesión regular

Resumen:

The advection-diffusion-reaction equation describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to advection, diffusion, reaction and forcing. This equation plays an important role in modelling the transport of a quasi-passive substance (for example, a pollutant) or a physical quantity (temperature, humidity, etc.) in the Earth’s atmosphere. In turn, the equations of nonlinear diffusion are widely used in modeling such processes as nonlinear combustion, rapid compression and accumulation of matter (laser fusion), chemical kinetics, magneto-hydrodynamics and many others. In particular, the fast-growing solutions of nonlinear diffusion equations can explain some important processes in demography (world population growth) and economics (rapid economic growth), meteorology (lightning and tornadoes) and ecology (growth of biological populations), epidemiology (outbreaks of infectious diseases) and neurophysiology, etc.

The implicit splitting-based 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 and in a spherical shell. Numerical experiments carried out on a high-resolution spherical mesh show the effectiveness of the method in modelling the dispersion of a pollutant 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 (Skiba et al., 2020). Although the scheme is implicit, the problem operator splitting method allows the construction of a fast-to-implementation direct (non-iterative) numerical algorithm.

References

1. Skiba YN. 2015. A non-iterative implicit algorithm for the solution of advection-diffusion equation on a sphere. International Journal for Numerical Methods in Fluids 78: 257-282. https://doi.org/10.1002/fld.4016

2. Skiba YN, Cruz-Rodriguez RC, Filatov DM, 2020. Solution of linear and nonlinear advection-diffusion problems on a sphere. Numerical Methods for Partial Differential Equations 36: 1922-1937. https://doi.org/10.1002/num.22510





Reunión Anual UGM 2022
30 de Octubre al 4 de Noviembre
Puerto Vallarta, Jalisco, México