scholarly journals Finger Growth and Selection in a Poisson Field

2019 ◽  
Vol 178 (3) ◽  
pp. 763-774
Author(s):  
N. R. McDonald
Keyword(s):  
Arbitrary Number ◽  
Numerical Results ◽  
Poisson’S Equation ◽  
Analogous Problem ◽  
Stat Phys ◽  
Two Dimensional ◽  
Poisson's Equation ◽  
Analytical Results ◽  
Poisson Field

AbstractSolutions are found for the growth of infinitesimally thin, two-dimensional fingers governed by Poisson’s equation in a long strip. The analytical results determine the asymptotic paths selected by the fingers which compare well with the recent numerical results of Cohen and Rothman (J Stat Phys 167:703–712, 2017) for the case of two and three fingers. The generalisation of the method to an arbitrary number of fingers is presented and further results for four finger evolution given. The relation to the analogous problem of finger growth in a Laplacian field is also discussed.

A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 393-406 ◽  
Author(s):  
Hu Li ◽  
Jin Huang
Keyword(s):  
Three Dimensional ◽  
High Accuracy ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Poisson's Equation ◽  
Mechanical Quadrature ◽  
Asymptotic Error ◽  
Accuracy Order ◽  
Mechanical Quadrature Method

AbstractIn this article, we consider the numerical solution for Poisson's equation in axisymmetric geometry. When the boundary condition and source term are axisymmetric, the problem reduces to solving Poisson's equation in cylindrical coordinates in the two-dimensional (r,z) region of the original three-dimensional domain S. Hence, the original boundary value problem is reduced to a two-dimensional one. To make use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular solution, which can be subtracted off, so that MQM can be used to solve the resulting Laplace problem, which possesses high accuracy order and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths hi is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by the splitting extrapolation algorithm (SEA). Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

Transonic Flow in Curved Channels

1967 ◽  
Vol 89 (4) ◽  
pp. 748-752 ◽  
Author(s):  
P. A. Thompson
Keyword(s):  
Transonic Flow ◽  
Approximate Calculation ◽  
Continuity Condition ◽  
Numerical Results ◽  
Two Dimensional ◽  
Curved Channels ◽  
Symmetric Channel ◽  
Analytical Results ◽  
Limiting Case

Transonic flow in a curved two-dimensional throat is considered. The approximate calculation is based on the full nonlinear inviscid equations and an integral continuity condition. Numerical results are presented in the form of curves which permit the determination of the flow in a nozzle of specified geometry. Analytical results reduce after linearization to those of Sauer for the limiting case of a symmetric channel.

A Variational Approach to the Two-Dimensional Nonlinear Poisson's Equation for the Modeling of Tunneling Transistors

2008 ◽  
Vol 29 (11) ◽  
pp. 1252-1255 ◽  
Author(s):  
Chen Shen ◽  
Sern-Long Ong ◽  
Chun-Huat Heng ◽  
G. Samudra ◽  
Yee-Chia Yeo
Keyword(s):  
Variational Approach ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Poisson's Equation

Two-dimensional model for predicting performance of aerated grit chambersA paper submitted to the Journal of Environmental Engineering and Science.

2009 ◽  
Vol 36 (9) ◽  
pp. 1567-1578 ◽  
Author(s):  
Alex Munoz ◽  
Stephanie Young
Keyword(s):  
Sensitivity Analysis ◽  
Velocity Field ◽  
Treatment Plant ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Poisson's Equation ◽  
Design Variables ◽  
Predicting Performance ◽  
Two Dimensional Model

A two-dimensional model was developed in this study. The model predicts the performance of a full-scale aerated grit chamber for grit removal from wastewater. The model numerically integrates Poisson’s equation, which describes the motion of the liquid induced by the rising air bubbles. The model makes use of finite element algorithms available in Mathcad to solve Poisson’s equation. The model was developed for predicting the velocity field in the chamber. The model was used to perform a sensitivity analysis of the design variables that affect the performance of an existing grit chamber at the Moose Jaw Wastewater Treatment Plant. The results of the sensitivity analysis indicate that predictions of velocity field are highly sensitive to energy transfer efficiency, air flowrate, and particle settling velocity but less sensitive to variations of wastewater flowrate, diffuser depth, and grid spacing.

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