In this paper we consider a modification to Darcy equation by taking into account the dependence of viscosity on the pressure. We present a stabilized mixed formulation for the resulting governing equations. Equal-order interpolation for the velocity and pressure is considered, and shown to be stable (which is not the case under the classical mixed formulation). The proposed mixed formulation i...

A cellular automaton model for the simulation of fluid flow in porous media is presented. A lattice and a set of rules are int roduced, such th at the flow equations in the continuum limit are formally the same as the equations for one-phase liquid flow in porous media. The model is valid in two as well as th ree dimensions. Numerical calculatio ns of some simple problems are presented and comp...

Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transfer external to a needle in porous medium have many biomedical engineering applications (e.g. hypodermic needles used hemotology). It is also design equipment's coating flows bio-inspired nanomaterials. Coating featuring combinations of nanoparticles motile micro-organisms constitute an important applic...

A new mixed nite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity This new mixed discretization ts the geometric shapes of the discontinuity of the rough coe cients and domain boundaries well This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas s mixed ni...

This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single ph...

A numerical method based on the modi®ed method of characteristics is developed for incompressible Darcy ̄ow. Fluid elements modeled as grid cells are mapped back in time to their twisted forms and a strict equality of volumes is imposed between the two. These relations are then cast in terms of potentials using Darcy's law and a nonlinear algebraic problem is solved for potentials. Though a gene...

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, i...

Bed shear stress in coarse–bed rivers with vegetation patches is one of the challenging parameters hydraulic engineering, mechanical fluvial morphology, and environmental studies. Based on this necessity, study, values bed four reaches Iran were estimated compared using methods boundary layer characteristics, logarithmic law, Darcy–Weisbach. Data collection study started February 2021 ended Apr...

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roug...