802 research outputs found
A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models
In this paper, a multiscale flux basis algorithm is developed to efficiently
solve a flow problem in fractured porous media. Here, we take into account a
mixed-dimensional setting of the discrete fracture matrix model, where the
fracture network is represented as lower-dimensional object. We assume the
linear Darcy model in the rock matrix and the non-linear Forchheimer model in
the fractures. In our formulation, we are able to reformulate the
matrix-fracture problem to only the fracture network problem and, therefore,
significantly reduce the computational cost. The resulting problem is then a
non-linear interface problem that can be solved using a fixed-point or
Newton-Krylov methods, which in each iteration require several solves of Robin
problems in the surrounding rock matrices. To achieve this, the flux exchange
(a linear Robin-to-Neumann co-dimensional mapping) between the porous medium
and the fracture network is done offline by pre-computing a multiscale flux
basis that consists of the flux response from each degree of freedom on the
fracture network. This delivers a conserve for the basis that handles the
solutions in the rock matrices for each degree of freedom in the fractures
pressure space. Then, any Robin sub-domain problems are replaced by linear
combinations of the multiscale flux basis during the interface iteration. The
proposed approach is, thus, agnostic to the physical model in the fracture
network. Numerical experiments demonstrate the computational gains of
pre-computing the flux exchange between the porous medium and the fracture
network against standard non-linear domain decomposition approaches
Geometric multigrid methods for Darcy-Forchheimer flow in fractured porous media
In this paper, we present a monolithic multigrid method for the efficient
solution of flow problems in fractured porous media. Specifically, we consider
a mixed-dimensional model which couples Darcy flow in the porous matrix with
Forchheimer flow within the fractures. A suitable finite volume discretization
permits to reduce the coupled problem to a system of nonlinear equations with a
saddle point structure. In order to solve this system, we propose a full
approximation scheme (FAS) multigrid solver that appropriately deals with the
mixed-dimensional nature of the problem by using mixed-dimensional smoothing
and inter-grid transfer operators. Remarkably, the nonlinearity is localized in
the fractures, and no coupling between the porous matrix and the fracture
unknowns is needed in the smoothing procedure. Numerical experiments show that
the proposed multigrid method is robust with respect to the fracture
permeability, the Forchheimer coefficient and the mesh size.Comment: arXiv admin note: text overlap with arXiv:1811.0126
Numerical discretization of a Darcy-Forchheimer problem coupled with a singular heat equation
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a
singular heat equation by a nonlinear forcing term depending on the
temperature. By singular we mean that the heat source corresponds to a Dirac
measure. We establish the existence of solutions for a model that allows a
diffusion coefficient in the heat equation depending on the temperature. For
such a model, we also propose a finite element discretization scheme and
provide an a priori convergence analysis. In the case that the aforementioned
diffusion coefficient is constant, we devise an a posteriori error estimator
and investigate reliability and efficiency properties. We conclude by devising
an adaptive loop based on the proposed error estimator and presenting numerical
experiments.Comment: arXiv admin note: text overlap with arXiv:2208.1288
MHD free convection-radiation interaction in a porous medium - part I : numerical investigation
A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by
laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented
by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic
in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient,
implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at
the mid points of net rectangles to get finite difference equations with a second order truncation error. We have
conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the
velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and
Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been
discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a
corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative
study between the previously published and present results in a limiting sense is found in an excellent agreement
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