For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and frequently calculate macroscopic parameters. More specifically, train with training set consisting of stochastic permeability realizations corresponding com...

Flow in discrete networks can be observed in biological, geological, or technical systems. Often, the number of individual segments is very large. Therefore, discrete pressure and flow calculation in each single segment becomes very time consuming, and a continuum model becomes attractive. We apply a global upscaling method based on a spatial average to investigate a porous media network model ...

New transmissibility upscaling procedures designed to accurately capture full-tensor effects are developed and applied. These techniques are based on variable compact multipoint (VCMP) flux approximations. VCMP is extended to irregular grids. Two approaches for including global flow information within the VCMP upscaling procedure are considered—one in which the upscaled model is determined dire...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

The transmission properties in two-dimensional plasma photonic crystal composed of and yttrium–iron–garnet rods with square lattices are demonstrated under different electron densities external magnetic fields. TE TM modes respond to the permittivity tensor permeability produced by field. For polarization, two distinct attenuation peaks appear ranges 3.4–3.62 GHz 3.78–4 GHz, induced fields, loc...

Background The use of a medical simulator should enhance the goals of minimally invasive surgery: patient safety, cosmesis, shortening the length of hospital admissions, and reducing cost. Using an innovative approach to the handling of ultrasound images in virtual reality simulation, this article describes a process that employs a hybrid model of deformable models that can be applied in the te...

We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

Accurate permeability estimation has always been a concern in determining flow units, assigning appropriate capillary pressure andrelative permeability curves to reservoir rock types, geological modeling, and dynamic simulation.Acoustic method can be used as analternative and effective tool for permeability determination. In this study, a four-step approach is proposed for permeability estimati...

Viscoelastic flows of polymer solutions in complex geometries can generate a strong localization stress within small regions the fluid and formation birefringent strands. In porous media, these localized structures drive preferential flow paths increase global dissipation. Modeling impact such effects at Darcy or larger scales is daunting task—one reasons being lack approaches using homogenizat...

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...