scholarly journals A Numerical Model with Finite Difference Schemes for Multi-Species Solute Transport in Porous Media

2021 ◽  
Author(s):  
Amin GHAREHBAGHI ◽  
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Finite Difference ◽  
Solute Transport ◽  
Decay Chain ◽  
Finite Difference Schemes ◽  
Suggested Model ◽  
One Dimensional ◽  
Homogeneous Porous Media ◽  
Order Scheme

A precise forecast of contaminant and solute transport has an inevitable role in the management of water resources. In accordance with this purpose, in this paper, a novel one-dimensional numerical model for the transport of a decay chain through homogeneous porous media is proposed. To develop the suggested model, two different schemes of the finite difference method, namely the Lax-Wendroff scheme and Fourth-Order scheme, are used. The verification and validation of the established model are examined by the analytical results of three multi-species solute dispersion problems with three- and four-chain members. The total mean square error, L2- and L∞-norms are applied to assess the results. Although analyses show that both schemes provided reliable results, the numerical results of the Lax-Wendroff scheme are more accurate.

2-D AUTOMATIC COMPOSITION OF NODAL VALUES FROM NUMERICAL MODEL USING SCRIPT PROGRAMMING

2013 ◽  
Vol 62 (1) ◽  
Author(s):  
Rudi Heriansyah
Keyword(s):  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Model ◽  
Finite Difference ◽  
Two Dimensional ◽  
Commercial Software ◽  
One Dimensional ◽  
Automatic Composition ◽  
The Individual ◽  
Individual Nodes

There are many commercial software to perform numerical modeling based on finite element (FEM) and finite difference (FDM) methods. It is often a requirement to the designer, that the values of the individual nodes in the numerical model are known. Usually, these softwares provide two methods to achieve this; firstly, by clicking directly onto the nodes of interest and secondly, by saving or exporting the whole nodal values to an external file. The former way is appropriate for models with small number of nodes, but as the number of nodes increases, it is no longer an efficient or effective way. Through the latter method, all nodal values are obtained, however the values are one-dimensional, and in some cases, only certain nodal values are required for presentation. In this paper, an algorithm for automatic composition of nodal values obtained from the second method mentioned above. The composed nodal values will be in two-dimensional form as this is the format used for uniform shaped model (square or rectangular). Since numerical softwares usually have facilities to save the data in a spreadsheet format, the proposed algorithm is implemented in this environment by using spreadsheet script programming.

scholarly journals NUMERICAL MODEL FOR AIR POLLUTION SIMULATION FROM ROAD TRANSPORT

2021 ◽  
Vol 1 (5(69)) ◽  
pp. 58-63
Author(s):  
M. Biliaiev ◽  
V. Biliaieva ◽  
O. Berlov ◽  
V. Kozachyna
Keyword(s):  
Air Pollution ◽  
Numerical Model ◽  
Finite Difference ◽  
Numerical Integration ◽  
Complex Terrain ◽  
Computer Code ◽  
Road Transport ◽  
Finite Difference Schemes ◽  
Air Pollution Modelling ◽  
Pollutant Transfer

The problem of air pollution modelling near road which is situated in complex terrain is under consideration. To simulate wind flow pattern in case of complex terrain Navier-Stokes’s equations were used. NavierStokes’s equations were written using Helmholtz variables. Numerical finite difference schemes of splitting were used for numerical integration of Navier-Stokes’s equations. Equation of connective-diffusive pollutant transfer was used to simulate air pollution. Finite difference scheme of splitting was used for numerical integration of convectivediffusive equation of pollutant transfer. Computer code was developed on the basis of created numerical model. The results of a numerical experiment are presented.

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