About: We propose stable and locally conservative hybrid mixed finite element methods to approximate the Darcy system and convection-diffusion problem, presented in a mixed form, to solve miscible displacements considering convective flows with adverse mobility ratio. The stability of the proposed formulations is achieved due to the choice of non-conforming Raviart-Thomas spaces combined to upwind scheme for the convection-dominated regimes, where the continuity conditions, between the elements, are weakly enforced by the introduction of Lagrange multipliers. Thus, the primal variables of both systems can be condensed in the element level leading a positive-definite global problem involving only the degrees of freedom associated with the multipliers. This approach, compared to the classical conforming Raviart-Thomas, present a reduction of the computational cost because, in both problems, the Lagrange multiplier is associated with a scalar field. In this context, a staggered algorithm is employed to decouple the Darcy problem from the convection-diffusion mixed system. However, both formulations are solved at the same time step, and the time discretization adopted for the convection-diffusion problem is the implicit backward Euler method. Numerical results show optimal convergence rates for all variables and the capacity to capture the formation and the propagation of the viscous fingering, as can be seen in the comparisons of the simulations of the Hele-Shaw cell with experimental results of the literature.   Goto Sponge  NotDistinct  Permalink

An Entity of Type : fabio:Abstract, within Data Space : wasabi.inria.fr associated with source document(s)

AttributesValues
type
value
  • We propose stable and locally conservative hybrid mixed finite element methods to approximate the Darcy system and convection-diffusion problem, presented in a mixed form, to solve miscible displacements considering convective flows with adverse mobility ratio. The stability of the proposed formulations is achieved due to the choice of non-conforming Raviart-Thomas spaces combined to upwind scheme for the convection-dominated regimes, where the continuity conditions, between the elements, are weakly enforced by the introduction of Lagrange multipliers. Thus, the primal variables of both systems can be condensed in the element level leading a positive-definite global problem involving only the degrees of freedom associated with the multipliers. This approach, compared to the classical conforming Raviart-Thomas, present a reduction of the computational cost because, in both problems, the Lagrange multiplier is associated with a scalar field. In this context, a staggered algorithm is employed to decouple the Darcy problem from the convection-diffusion mixed system. However, both formulations are solved at the same time step, and the time discretization adopted for the convection-diffusion problem is the implicit backward Euler method. Numerical results show optimal convergence rates for all variables and the capacity to capture the formation and the propagation of the viscous fingering, as can be seen in the comparisons of the simulations of the Hele-Shaw cell with experimental results of the literature.
Subject
  • Computational fluid dynamics
  • Partial differential equations
  • Numerical differential equations
  • Parabolic partial differential equations
part of
is abstract of
is hasSource of
Faceted Search & Find service v1.13.91 as of Mar 24 2020


Alternative Linked Data Documents: Sponger | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data]
OpenLink Virtuoso version 07.20.3229 as of Jul 10 2020, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (94 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software