scholarly journals Non-linear multi-point flux approximation in the near-well region

Filomat ◽  
2018 ◽  
Vol 32 (20) ◽  
pp. 6857-6867
Author(s):  
Milan Dotlic ◽  
Boris Pokorni ◽  
Milenko Pusic ◽  
Milan Dimkic
Keyword(s):  
Porous Medium ◽  
Maximum Principle ◽  
Anisotropic Medium ◽  
Hydraulic Head ◽  
Second Order ◽  
Flow Simulations ◽  
Flux Approximation ◽  
Non Linear ◽  
Anisotropic Porous Medium ◽  
Hydraulic Head Distribution

We consider non-linear multi-point flux approximations (MPFA) scheme for flow simulations in a model of anisotropic porous medium that includes wells. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Due to this strong non-linearity of the near-well flow, use of the MPFA scheme in the near well region results in a completely wrong total well flux and an inaccurate hydraulic head distribution. In this article we propose correction of the MPFA scheme. The outcome is a scheme that is second-order accurate even in the well vicinity for anisotropic medium. Solution obtained with this scheme respects minimum and maximum principle, and also, it is non-oscillating.

Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

2014 ◽  
Vol 14 (4) ◽  
pp. 473-483 ◽  
Author(s):  
Milan Dotlić
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Hydraulic Head ◽  
Anisotropic Porous Media ◽  
Flow Simulations ◽  
First Order ◽  
Anisotropic Porous Medium ◽  
Volume Method

AbstractWe consider a finite volume method for flow simulations in an anisotropic porous medium in the presence of a well. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Thus, the use of standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. In this article we propose two finite volume methods to model the well singularity in an anisotropic medium. The first method significantly reduces the total well flux error, but the hydraulic head is still not even first-order accurate. The second method gives a second-order accurate hydraulic head and at least first-order accurate total well flux.

scholarly journals Non-linear Stability in Transitional and Rotatory Regime of the Cooking of Gari, Food Based on Cassava Tubers

2021 ◽  
pp. 30-39
Author(s):  
Vodounnou Edmond Claude ◽  
Djossou Ayihaou Armand ◽  
Semassou Guy Clarence ◽  
Degan Gérard
Keyword(s):  
Porous Medium ◽  
Linear Stability ◽  
Taylor Number ◽  
Temperature Fields ◽  
Cassava Flour ◽  
Cooking Process ◽  
Non Linear ◽  
Anisotropic Porous Medium ◽  
Anisotropy Parameters ◽  
Over Time

The present study focuses on the non-linear stability in the transient rotary regime of the cooking process of gari. The process of cooking gari consists of a rotating rectangular cavity filled with grated cassava flour, pressed, retted and considered to be an anisotropic porous medium in a permeably saturated viscoelastic fluid. The cavity is heated from below to a constant temperature. The lower wall of the cavity is impermeable and the upper wall is permeable. Using a numerical method, we have established the transient expressions of the Nusselt number, the flow and temperature fields as a function of the anisotropy parameters of the porous medium and of the Taylor number. The results obtained showed that the anisotropy of the porous medium and the Taylor number greatly influenced the cooking of gari over time.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

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