Least square-based finite volumes for solving the advection–diffusion of contaminants in porous media

2004 ◽  
Vol 51 (4) ◽  
pp. 451-461 ◽  
Author(s):  
Enrico Bertolazzi ◽  
Gianmarco Manzini
Keyword(s):  
Porous Media ◽  
Least Square ◽  
Finite Volumes ◽  
Advection Diffusion

A New Particle Set of Contours Method for Advection-Diffusion Problems Applied to the Modelling of Waste Disposal

2012 ◽  
Author(s):  
Héloise Beaugendre ◽  
Serge Huberson ◽  
Iraj Mortazavi
Keyword(s):  
Porous Media ◽  
Waste Disposal ◽  
Particle Method ◽  
Linear Diffusion ◽  
Bench Tests ◽  
Diffusion Operator ◽  
Advection Diffusion ◽  
Conservative Form ◽  
Transport Problems ◽  
Diffusion Problems

In this work a particle sets of contours method is coupled to a streamline technique in order to obtain accurate approximations of transport problems. A modified streamlines technique is proposed and several bench tests arising in porous media are then simulated to validate the new method. These results are complemented with the resolution of the diffusion operator in a non conservative form where the non-linear diffusion operator is transformed in a velocity-like term and solved using this new particle method. The method is then used to model transport in porous media applied to the waste disposal.

scholarly journals Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 511
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Porous Media ◽  
Soil Water ◽  
Water Flow ◽  
Water Movement ◽  
Least Square ◽  
Flow In Porous Media ◽  
Fickian Diffusion ◽  
Richards Equation ◽  
Governing Equations ◽  
Soil Water Flow

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.

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