scholarly journals Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

2000 ◽  
Vol 2 (4) ◽  
pp. 255-267 ◽  
Author(s):  
B. Lin ◽  
S. N. Chandler-Wilde
Keyword(s):  
Water Quality ◽  
Mesh Generation ◽  
Least Squares Method ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Numerical Conformal Mapping ◽  
Numerical Examples ◽  
Multiply Connected ◽  
Polygonal Region ◽  
Multiply Connected Regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

scholarly journals Circular Slits Map of Bounded Multiply Connected Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ali W. K. Sangawi ◽  
Ali H. M. Murid ◽  
M. M. S. Nasser
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Connected Region ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

We present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a circular slit region. The method is based on some uniquely solvable boundary integral equations with adjoint classical, adjoint generalized, and modified Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method.

scholarly journals A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohamed M. S. Nasser ◽  
Ali H. M. Murid ◽  
Samer A. A. Al-Hatemi
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
Numerical Examples ◽  
Multiply Connected ◽  
Generalized Neumann Kernel ◽  
Multiply Connected Regions ◽  
Neumann Kernel

We present a uniquely solvable boundary integral equation with the generalized Neumann kernel for solving two-dimensional Laplace’s equation on multiply connected regions with mixed boundary condition. Two numerical examples are presented to verify the accuracy of the proposed method.

scholarly journals Numerical Conformal Mapping of Unbounded Multiply Connected Regions onto Circular Slit Regions

2014 ◽  
Vol 8 (1) ◽  
Author(s):  
A.A.M. Yunus ◽  
A.H.M. Murid ◽  
M.M. S. Nasser
Keyword(s):  
Conformal Mapping ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

This paper presents a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto circular slit regions. Three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the classical and the adjoint generalized Neumann kernels. Several numerical examples are presented.

Numerical conformal mapping of multiply connected regions by Fornberg-like methods

1999 ◽  
Vol 83 (2) ◽  
pp. 205-230 ◽  
Author(s):  
Thomas K. DeLillo ◽  
Mark A. Horn ◽  
John A. Pfaltzgraff
Keyword(s):  
Conformal Mapping ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Multiply Connected Regions

scholarly journals Treatment Efficiency of Diffuse Agricultural Pollution in a Constructed Wetland Impacted by Groundwater Seepage

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1601 ◽  
Author(s):  
Keit Kill ◽  
Jaan Pärn ◽  
Rauno Lust ◽  
Ülo Mander ◽  
Kuno Kasak
Keyword(s):  
Water Quality ◽  
Typha Latifolia ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Agricultural Pollution ◽  
Total Inorganic Carbon ◽  
Treatment Efficiency ◽  
Effective Measure ◽  
Groundwater Seepage ◽  
P Removal

Diffuse agricultural pollution degrades water quality and is one of the main causes of eutrophication; therefore, it is important to reduce it. Constructed wetlands (CW) can be used as an effective measure for water quality improvement. There are two possible ways to establish surface flow CWs, in-stream and off-stream. We studied treatment efficiency of the in-stream free surface flow (FSW) Vända CW in southern Estonia from March 2017 until July 2018. The CW consists of two shallow-water parts planted with cattail (Typha latifolia). According to our analyses, the CW reduced total phosphorus (TP) and phosphate (PO4-P) by 20.5% and 16.3%, respectively, however, in summer, phosphorus removal was twice as high. We saw significant logarithmic correlation between flow rates and log TP and log PO4-P removal efficiency (rs = 0.53, rs = 0.63, p < 0.01 respectively). Yearly reduction of total organic carbon was 12.4% while total inorganic carbon increased by 9.7% due to groundwater seepage. Groundwater inflow also increased the concentration of total nitrogen in the outlet by 27.7% and nitrate concentration by 31.6%. In-stream FWS CWs are a promising measure to reduce diffuse pollution from agriculture; however, our experience and literature data prove that there are several factors that can influence CWs’ treatment efficiency.

Analysis of Polygonal Vortex Flows in a Cylinder with a Rotating Bottom

2021 ◽  
Vol 11 (3) ◽  
pp. 1348
Author(s):  
A. Rashkovan ◽  
S.D. Amar ◽  
U. Bieder ◽  
G. Ziskind
Keyword(s):  
Experimental Studies ◽  
Free Surface Flow ◽  
Careful Analysis ◽  
Numerical Approach ◽  
Surface Flow ◽  
Initial Water ◽  
Eddy Simulation ◽  
Disk Rotation ◽  
Inner Radius ◽  
Liquid Flows

The present paper provides a physically sound numerical modeling of liquid flows experimentally observed inside a vertical circular cylinder with a stationary envelope, rotating bottom and open top. In these flows, the resulting vortex depth may be such that the rotating bottom disk becomes partially exposed, and rather peculiar polygon shapes appear. The parameters and features of this work are chosen based on a careful analysis of the literature. Accordingly, the cylinder inner radius is 145 mm and the initial water height is 60 mm. The experiments with bottom disk rotation frequencies of 3.0, 3.4, 4.0 and 4.6 Hz are simulated. The chosen frequency range encompasses the regions of ellipse and triangle shapes as observed in the experimental studies reported in the literature. The free surface flow is expected to be turbulent, with the Reynolds number of O(105). The Large Eddy Simulation (LES) is adopted as the numerical approach, with a localized dynamic Subgrid-Scale Stresses (SGS) model including an energy equation. Since the flow obviously requires a surface tracking or capturing method, a volume-of-fluid (VOF) approach has been chosen based on the findings, where this method provided stable shapes in the ranges of parameters found in the corresponding experiments. Expected ellipse and triangle shapes are revealed and analyzed. A detailed character of the numerical results allows for an in-depth discussion and analysis of the mechanisms and features which accompany the characteristic shapes and their alterations. As a result, a unique insight into the polygon flow structures is provided.

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