scholarly journals FLUSHING PATTERN OF NON-REACTIVE EFFLUENTS

1970 ◽  
Vol 1 (12) ◽  
pp. 113
Author(s):  
Adel M. Kamel
Keyword(s):  
Numerical Model ◽  
Finite Difference ◽  
Temporal Variations ◽  
Phase Lag ◽  
Tidal Variation ◽  
One Dimensional ◽  
South Central ◽  
Reactive Liquid ◽  
Explicit Finite Difference ◽  
Good Agreement

In south central Louisiana non-reactive liquid effluents are introduced into man-made relatively straight prismatic canals which are comparatively narrow and have brackish watpr To study the flushing pattern of liquid effluents introduced into those canals (or eptuanes), a one-dimensional numerical model is considered for a simplified system consisting of a long straight gently sloping reach with a sinusoidal tidal variation at the mouth of the estuary, sinusoidal tidal v^iation with a phase lag and an attenuated amplitude at the upstream end, a variable inflow hydrograph, and a variable inflow or outflow. For this system, the continuity and momentum eauations are solved numerically by an explicit finite difference scheme. The output of the model describes the spatial and temporal variations in flow velocity (also in water depth and discharge) from which the flushing pattern is obtained for a liquid effluent introduced at any time during the tidal cycle at any section along the estuary. The numerical model is applied to Charenton drainage canal m south central Louisiana and good agreement is obtained between the velocities and stage elevations predicted from the model and recorded in the field. An IBIV 360/65 computer is utilized.

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 A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

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