scholarly journals Analytical solution for the stationary model of pollutant propagation in an aquatic medium

2019 ◽  
Vol 14 (2) ◽  
pp. 1
Author(s):  
Cíntia Ourique Monticelli ◽  
Jorge Rodolfo Zabadal ◽  
Daniela Muller Quevedo ◽  
Carlos Augusto Nascimento
Keyword(s):  
Stream Function ◽  
Concentration Distribution ◽  
Pollutant Dispersion ◽  
Curvilinear Coordinates ◽  
Qualitative Behavior ◽  
Inviscid Flows ◽  
Advection Diffusion Equation ◽  
Thermotolerant Coliforms ◽  
Orthogonal Curvilinear Coordinates ◽  
Pollutant Propagation

This work presents a new analytical approach for solving pollutant dispersion problems along irregular-shaped water bodies. In this approach, the advection-diffusion equation is expressed in terms of orthogonal curvilinear coordinates, defined by the velocity potential and the corresponding stream function for inviscid flows. The boundary condition rewritten in terms of these new coordinates is reduced to a classical third kind one, i.e., the derivative of the concentration distribution with respect to the stream function is proportional to the numerical value of the local pollutant concentration. The solution obtained from the proposed formulation was employed to simulate pollutant dispersion (thermotolerant coliforms) along the Pampa Creek, a tributary of the Sinos River at the outskirts of Novo Hamburgo city, South Region of Brazil. The results obtained reproduce the qualitative behavior of the expected concentration distribution.

scholarly journals Transonic Flow Along Arbitrary Stream Filament of Revolution Solved by Separate Computations With Shock Fitting

1986 ◽  
Author(s):  
Wang Baoguo ◽  
Hua Yaonan ◽  
Huang Xiaoyan ◽  
Wu Chung-Hua
Keyword(s):  
Flow Field ◽  
Stream Function ◽  
Transonic Flow ◽  
Matrix Method ◽  
Axial Compressor ◽  
Iteration Scheme ◽  
Curvilinear Coordinates ◽  
Algebraic Equations ◽  
Compressor Rotor ◽  
Orthogonal Curvilinear Coordinates

The transonic flow field in a cascade of blades lying on an S1 stream surface of revolution is solved by separate computations in the supersonic and the transonic region. The characteristics method is used to solve the supersonic flow upstream of the passage shock and the direct matrix method is used to solve the transonic flow downstream of the passage shock. The transonic stream-function equation in weak conservative form was discretized with respect to general non-orthogonal curvilinear coordinates. Using the artificial density technique and a new iteration scheme between the stream function and the density, the set of algebraic equations was solved by the direct matrix method. A computer program has been developed and is applied to compute the flow field on several S1 stream surfaces of revolution for the DFVLR transonic axial compressor rotor. It is found that the thickness of the S1 stream filament and the variation of entropy along the streamlines have strong influence on calculation. The calculated result agrees with the experimental data fairly well.

scholarly journals A Stream Function Relaxation Method for Solving Transonic S1 Stream Surface With Pre-Determination of the Density

1985 ◽  
Author(s):  
Ge Manchu
Keyword(s):  
Difference Scheme ◽  
Stream Function ◽  
Flow Theory ◽  
Relaxation Method ◽  
Curvilinear Coordinates ◽  
Transonic Flows ◽  
Stream Surface ◽  
Numerical Examples ◽  
Orthogonal Curvilinear Coordinates

On the basis of Prof. Wu’s 3-D flow theory (ref.1, 2, 3, 4, 5), a general streamfunction equation in non-orthogonal curvilinear coordinates is developed. The equation can be used to calculate subsonic or transonic flows on S1 or S2 stream surfaces of turbomachinery. In this paper streamlines coordinates and a mixed difference scheme are adopted in solving the stream function equation. A procedure for pre-determination of the density is developed and used to determine the unique-value of density from the known value of the stream function. Numerical examples are given.

scholarly journals A high-precision algorithm for axisymmetric flow

1995 ◽  
Vol 1 (1) ◽  
pp. 11-25
Author(s):  
A. Gokhman ◽  
D. Gokhman
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Stream Function ◽  
Potential Flow ◽  
Axisymmetric Flow ◽  
Curvilinear Coordinates ◽  
Shape Functions ◽  
Quadrilateral Elements ◽  
Orthogonal Curvilinear Coordinates ◽  
Double Integrals

We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.

XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates

1927 ◽  
Vol 46 ◽  
pp. 194-205 ◽  
Author(s):  
C. E. Weatherburn
Keyword(s):  
Curvilinear Coordinates ◽  
Triple Systems ◽  
Orthogonal Curvilinear Coordinates ◽  
Orthogonal Systems ◽  
Considerable Detail

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

2011 ◽  
Vol 130-134 ◽  
pp. 2993-2996
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Solution Procedure ◽  
Dam Break ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Proposed Model ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Orthogonal Curvilinear Coordinates ◽  
Averaged Model ◽  
The Mathematical Model

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.

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