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A FIVE-FIELD AUGMENTED FULLY-MIXED FINITE ELEMENT METHOD FOR THE NAVIER-STOKES/DARCY COUPLED PROBLEM

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dc.creatorNATHALIE ALEJANDRA VALENZUELA CACHICAS
dc.creatorRICARDO ELVIS OYARZÚA VARGAS
dc.date2020
dc.date.accessioned2025-01-10T15:15:40Z
dc.date.available2025-01-10T15:15:40Z
dc.date.issued2020
dc.description.abstractIN THIS WORK WE INTRODUCE AND ANALYZE A NEW AUGMENTED FULLY-MIXED FORMULATION FOR THE STATIONARY NAVIER?STOKES/DARCY COUPLED PROBLEM. OUR APPROACH EMPLOYS, ON THE FREE-FLUID REGION, A TECHNIQUE PREVIOUSLY APPLIED TO THE STATIONARY NAVIER?STOKES EQUATIONS, WHICH CONSISTS OF THE INTRODUCTION OF A MODIFIED PSEUDOSTRESS TENSOR INVOLVING THE DIFFUSIVE AND CONVECTIVE TERMS, TOGETHER WITH THE PRESSURE. IN ADDITION, BY USING THE INCOMPRESSIBILITY CONDITION, THE PRESSURE IS ELIMINATED, AND SINCE THE CONVECTIVE TERM FORCES THE FREE-FLUID VELOCITY TO LIVE IN A SMALLER SPACE THAN USUAL, WE AUGMENT THE RESULTING FORMULATION WITH SUITABLE GALERKIN TYPE TERMS ARISING FROM THE CONSTITUTIVE AND EQUILIBRIUM EQUATIONS. ON THE OTHER HAND, IN THE DARCY REGION WE APPLY THE USUAL DUAL-MIXED FORMULATION, WHICH YIELDS THE INTRODUCTION OF THE TRACE OF THE POROUS MEDIA PRESSURE AS AN ASSOCIATED LAGRANGE MULTIPLIER. THE LATTER IS CONNECTED WITH THE FACT THAT ONE OF THE TRANSMISSION CONDITIONS INVOLVING MASS CONSERVATION BECOMES ESSENTIAL AND MUST BE IMPOSED WEAKLY. IN THIS WAY, WE OBTAIN A FIVE-FIELD FORMULATION WHERE THE PSEUDOSTRESS AND THE VELOCITY IN THE FLUID, TOGETHER WITH THE VELOCITY AND THE PRESSURE IN THE POROUS MEDIUM, AND THE AFOREMENTIONED LAGRANGE MULTIPLIER, ARE THE CORRESPONDING UNKNOWNS. THE WELL-POSEDNESS ANALYSIS IS CARRIED OUT BY COMBINING THE CLASSICAL BABU?KA?BREZZI THEORY AND THE BANACH FIXED-POINT THEOREM. A PROPER ADAPTATION OF THE ARGUMENTS EXPLOITED IN THE CONTINUOUS ANALYSIS ALLOWS US TO STATE SUITABLE HYPOTHESES ON THE FINITE ELEMENT SUBSPACES ENSURING THAT THE ASSOCIATED GALERKIN SCHEME IS WELL-POSED AND CONVERGENT. IN PARTICULAR, RAVIART?THOMAS ELEMENTS OF LOWEST ORDER FOR THE PSEUDOSTRESS AND THE DARCY VELOCITY, CONTINUOUS PIECEWISE LINEAR POLYNOMIALS FOR THE FREE-FLUID VELOCITY, PIECEWISE CONSTANTS FOR THE DARCY PRESSURE, TOGETHER WITH CONTINUOUS PIECEWISE LINEAR ELEMENTS FOR THE LAGRANGE MULTIPLIER, CONSTITUTE FEASIBLE CHOICES. FINALLY, WE PROVIDE SEVERAL NUME
dc.formatapplication/pdf
dc.identifier.doi10.1016/j.camwa.2020.08.017
dc.identifier.issn1873-7668
dc.identifier.issn0898-1221
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/11173
dc.languagespa
dc.publisherCOMPUTERS & MATHEMATICS WITH APPLICATIONS
dc.relation.uri10.1016/j.camwa.2020.08.017
dc.rightsPUBLICADA
dc.titleA FIVE-FIELD AUGMENTED FULLY-MIXED FINITE ELEMENT METHOD FOR THE NAVIER-STOKES/DARCY COUPLED PROBLEM
dc.title.alternativeUN MÉTODO DE ELEMENTOS FINITOS TOTALMENTE MEZCLADOS AUMENTADOS DE CINCO CAMPOS PARA EL PROBLEMA ACOPLADO NAVIER-STOKES/DARCY
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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