Abstract—This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers r...

The subject of this paper is a first-order system least-squares formulation for the Stokes equation which remains uniformly valid in the limit of vanishing viscosity. For this so-called Darcy-Stokes flow problem we establish continuity and coercivity of the corresponding least-squares functional in appropriate norms. Two types of finite element spaces for the approximation of the velocity field...

Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report nonlinear Darcy law as function pressure gradient. this letter we consider treelike structure for which problem can be resolved exactly due to mapping with directed polymer (DP) disordered bond energies on Cayley tree. Our results confirm beha...

An analytical solution for moisture dynamic during freeze-drying based in non-ideal Darcy’s law that resolves the singularity at zero time was deducted. The is represented by a pseudo permeability (K∗) and deviation index (n). must be complemented with numerical of Fourier’s equations heat transfer two product zones. model fitted to experimental dynamics an orange juice-based cake. obtained K∗=...

We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation ut −∆ u ∈ a H(u − μ) in Q = Ω × (0, T ], whereΩ ⊂ Rn is a ring-shaped domain, a andμ are given positive constants,H(·) is the Heaviside maximal monotone graph:H(s) = 1 if s > 0,H(0) = [0, 1],H(s) = 0 if s < 0. Such equations arise in climatology (the so-called Budyko energy balance model), as we...

The kinematic viscosity is a major physical property to be used in numerical, experimental and analytical work in all the related fields of fluid flow research. Its determination can be based on experiments with viscometer and on calculations for single or multi-species components, possibly through the use of mixture law and other intermediate parameters. Its experimental estimation for multi-s...

In this report, a partitioned time stepping algorithm which allows different time steps in the fluid region and the porous region is analyzed for the fully evolutionary Stokes-Darcy problem. This method requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove ze...

In this report, a partitioned time stepping algorithm for transient flow in a porous medium coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires only solve one, uncoupled Stokes and Darcy sub-physics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph int...

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation law and the Darcy ́s law. This equation may be written in three standard forms: the “h-based” form, the “θ-based” form, and the “mixed” form. Numerical aproximations based on different forms of this one-dimensional nonlinear equation can lead to significantly diffe...

Mixed finite-element methods are attractive for modeling flows in porous media since they can yield pressures and velocities having comparable accuracy. In solving the resulting discrete equations, however, poor matrix conditioning can arise both from spatial heterogeneity in the medium and from the fine grids needed to resolve that heterogeneity. This paper presents two iterative schemes that ...