Filtration Calculations for Water Development Projects: Software Package

1991 ◽  
Vol 24 (10) ◽  
pp. 291-293
Author(s):  
Tatyana G. Shvachich
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Substantial Reduction ◽  
Development Projects ◽  
Filtration Flow ◽  
Two Dimensional ◽  
Source Information ◽  
Water Development ◽  
Homogeneous Porous Medium ◽  
Initial And Boundary Conditions

The system as a means of automated calculation of groundwater filtration in non-homogeneous porous medium with arbitrary initial and boundary conditions is provided. The package consists of a series of modules. The programs are developed for designing screened dams and are characterized by a substantial reduction of input data volume. The package is successfully used for designing of water development projects, providing a means of maintaining and analysing different antifiltration techniques, namely: screens, upstream floors (fores), flow cores, cutoff walls, concrete screens, etc. while constnacting dams and water development structures of arbitrary contours. This particular package is designed to provide automated calculation of groundwater filtration in non-homogeneous porous medium with arbitrary initial and boundary conditions. The system can also provide a means of computing the two-dimensional filtration flow in water development structures such as dams, concrete structures and the like. The package consists of a series of modules for designing the filtration effect in water development projects with both multi-layered and homogeneous basements, simulating the two-dimensional discontinuity filtration flows (screened dams particularly), plotting the hydrodynamic grid. The modules provide capabilities for determining:–depression curve coordinates, i.e. basic data for calculation of slope stability and the proper slope geometry depending on underground freezing severity are provided;–filtration rates and the maximum values, i.e. the source information for calculating antisuffosion ground stability is provided;–head gradients and the peak values;–areas of all the cross-section elements;–field of heads;–back pressure values;–field of flow function, i.e. the value of a filtration flow rate in a zone between a water confining layer and a given field point;– water development structure shear strength.

Mathematical modeling of fluid flows through the piecewise homogeneous porous medium by R-function method

2021 ◽  
Vol 8 (3) ◽  
pp. 499-508
Author(s):  
O. R. Podhornyj ◽  
◽  
M. V. Sidorov ◽  
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Stream Function ◽  
Solution Structure ◽  
Complete Solution ◽  
Ritz Method ◽  
Homogeneous Porous Medium ◽  
Type Boundary ◽  
Integral Ratio ◽  
R Functions

The stationary fluid flow through a piecewise homogeneous porous medium is considered under the assumption that Darcy's law holds. The mathematical model of this problem is defined as an elliptic equation for the stream function, supplemented by the second-type boundary conditions at the water boundaries and the first-type boundary conditions at the impervious to liquid boundaries. The problem statement also includes the conditions of conjugation at the separation line between two soils and the unknown value of fluid discharge, which can be established from the additional integral ratio. It is proposed to use the structure-variational method of R-functions in order to numerically analyze and solve the current problem. The complete solution structure for the boundary value problem of stream function regarding the R-functions method is established, moreover, the application of the Ritz method for approximating an unspecified structural formula component is substantiated. Then, the approximate value of the fluid discharge and the approximate solution of the original problem are found from the additional integral ratio. The computational experiment was carried out with different coefficients of permeability within the area, which has the shape of the lower half ring. It is established that as the number of coordinate functions increases, the value of fluid discharge becomes constant, indicating the convergence of the proposed method.

scholarly journals Well-posedness of the Muskat problem in subcritical L p -Sobolev spaces

2021 ◽  
pp. 1-43
Author(s):  
H. ABELS ◽  
B.-V. MATIOC
Keyword(s):  
Porous Medium ◽  
Vertical Motion ◽  
Parabolic Type ◽  
Immiscible Fluids ◽  
Well Posedness ◽  
Two Dimensional ◽  
Critical Space ◽  
Smoothing Property ◽  
Muskat Problem ◽  
Homogeneous Porous Medium

We study the Muskat problem describing the vertical motion of two immiscible fluids in a two-dimensional homogeneous porous medium in an L p -setting with p ∈ (1, ∞). The Sobolev space $W_p^s(\mathbb R)$ with s = 1+1/p is a critical space for this problem. We prove, for each s ∈ (1+1/p, 2) that the Rayleigh–Taylor condition identifies an open subset of $W_p^s(\mathbb R)$ within which the Muskat problem is of parabolic type. This enables us to establish the local well-posedness of the problem in all these subcritical spaces together with a parabolic smoothing property.

Flow of a non-homogeneous fluid in a porous medium

1961 ◽  
Vol 10 (1) ◽  
pp. 133-140 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Variable Viscosity ◽  
Practical Importance ◽  
Specific Weight ◽  
Steady Flows ◽  
Two Dimensional ◽  
Homogeneous Fluid ◽  
Non Linear ◽  
Two Dimensional Flows

If the viscosity and specific weight of a fluid are variable, the equations governing its flow in a porous medium are non-linear and in general very difficult to solve. It has been found, however, that steady flows of a fluid of variable viscosity but constant specific weight can be reduced to those of a homogeneous fluid by a remarkably simple transformation, which indicates that the flow patterns of the fluid are the same as those of a homogeneous fluid with the same boundary conditions, and that only the speed need be modified. The speed of the actual flow is obtained by dividing the speed of the homogeneous-fluid flow by a factor proportional to the actual viscosity. The transformation is also used to derive the equations governing steady two-dimensional flows and steady axisymmetric flows of a fluid of variable viscosity and specific weight. In a good many cases of practical importance these equations are exactly linear, in spite of the fact that the governing equations obtained without the use of the above-mentioned transformation are non-linear. An exact solution for a steady two-dimensional flow with prescribed boundary conditions is given. Two inverse methods for generating exact solutions for two-dimensional flows are presented, together with two illustrative examples. The theory also applies to Hele-Shaw flows, so that it can be easily verified in the laboratory.

Modelling Of Transport And Capture Of Particles In A Porous Medium

2019 ◽  
pp. 56-60
Keyword(s):  
Porous Medium ◽  
Asymptotic Solution ◽  
Retention Mechanism ◽  
Inverse Filtering ◽  
Underground Structures ◽  
Loose Soil ◽  
Monodisperse Suspension ◽  
Homogeneous Porous Medium ◽  
Model Equations ◽  
Pass Through

The study of the transport and capture of particles moving in a fluid flow in a porous medium is an important problem of underground hydromechanics, which occurs when strengthening loose soil and creating watertight partitions for building tunnels and underground structures. A one-dimensional mathematical model of long-term deep filtration of a monodisperse suspension in a homogeneous porous medium with a dimensional particle retention mechanism is considered. It is assumed that the particles freely pass through large pores and get stuck at the inlet of small pores whose diameter is smaller than the particle size. The model takes into account the change in the permeability of the porous medium and the permissible flow through the pores with increasing concentration of retained particles. A new spatial variable obtained by a special coordinate transformation in model equations is small at any time at each point of the porous medium. A global asymptotic solution of the model equations is constructed by the method of series expansion in a small parameter. The asymptotics found is everywhere close to a numerical solution. Global asymptotic solution can be used to solve the inverse filtering problem and when planning laboratory experiments.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium
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