Publicación:
ON A VORTICITY-BASED FORMULATION FOR REACTION-DIFFUSION-BRINKMAN SYSTEMS

dc.creatorVERÓNICA JULIA ANAYA DOMÍNGUEZ
dc.creatorDAVID ANDRÉS MORA HERRERA
dc.date2018
dc.date.accessioned2025-01-10T14:57:41Z
dc.date.available2025-01-10T14:57:41Z
dc.date.issued2018
dc.description.abstractWE ARE INTERESTED IN MODELLING THE INTERACTION OF BACTERIA AND CERTAIN NUTRIENT CONCENTRATION WITHIN A POROUS MEDIUM ADMITTING VISCOUS FLOW. THE GOVERNING EQUATIONS IN PRIMAL-MIXED FORM CONSIST OF AN ADVECTION-REACTION-DIFFUSION SYSTEM REPRESENTING THE BACTERIA-CHEMICAL MASS EXCHANGE, COUPLED TO THE BRINKMAN PROBLEM WRITTEN IN TERMS OF FLUID VORTICITY, VELOCITY AND PRESSURE, AND DESCRIBING THE FLOW PATTERNS DRIVEN BY AN EXTERNAL SOURCE DEPENDING ON THE LOCAL DISTRIBUTION OF THE CHEMICAL SPECIES. A PRIORI STABILITY BOUNDS ARE DERIVED FOR THE UNCOUPLED PROBLEMS, AND THE SOLVABILITY OF THE FULL SYSTEM IS ANALYSED USING A FIXED-POINT APPROACH. WE INTRODUCE A PRIMAL-MIXED FINITE ELEMENT METHOD TO NUMERICALLY SOLVE THE MODEL EQUATIONS, EMPLOYING A PRIMAL SCHEME WITH PIECEWISE LINEAR APPROXIMATION OF THE REACTION-DIFFUSION UNKNOWNS, WHILE THE DISCRETE FLOW PROBLEM USES A MIXED APPROACH BASED ON RAVIART-THOMAS ELEMENTS FOR VELOCITY, NÉDÉLEC ELEMENTS FOR VORTICITY, AND PIECEWISE CONSTANT PRESSURE APPROXIMATIONS. IN PARTICULAR, THIS CHOICE PRODUCES EXACTLY DIVERGENCE-FREE VELOCITY APPROXIMATIONS. WE ESTABLISH EXISTENCE OF DISCRETE SOLUTIONS AND SHOW THEIR CONVERGENCE TO THE WEAK SOLUTION OF THE CONTINUOUS COUPLED PROBLEM. FINALLY, WE REPORT SEVERAL NUMERICAL EXPERIMENTS ILLUSTRATING THE BEHAVIOUR OF THE PROPOSED SCHEME.
dc.formatapplication/pdf
dc.identifier.doi10.3934/nhm.2018004
dc.identifier.issn1556-181X
dc.identifier.issn1556-1801
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/9754
dc.languagespa
dc.publisherNetworks and Heterogeneous Media
dc.relation.uri10.3934/nhm.2018004
dc.rightsPUBLICADA
dc.titleON A VORTICITY-BASED FORMULATION FOR REACTION-DIFFUSION-BRINKMAN SYSTEMS
dc.title.alternativeSOBRE UNA FORMULACIÓN BASADA EN LA VORTICIDAD PARA SISTEMAS DE REACCIÓN-DIFUSIÓN-BRINKMAN
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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