A control volume method to solve an elliptic equation on a two-dimensional irregular mesh

1992 ◽  
Vol 100 (2) ◽  
pp. 275-290 ◽  
Author(s):  
I. Faille
Keyword(s):  
Elliptic Equation ◽  
Control Volume ◽  
Two Dimensional ◽  
Control Volume Method ◽  
Irregular Mesh ◽  
Volume Method

Computational Fluid Dynamics-Heat Transfer Meshless Control Volume Method

2004 ◽  
Author(s):  
Ali Arefmanesh ◽  
Mohammad Najafi ◽  
Hooman Abdi
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Control Volume ◽  
Numerical Technique ◽  
Computational Domain ◽  
Two Dimensional ◽  
Control Volume Method ◽  
Control Volumes ◽  
Volume Method

A novel meshless numerical technique to solve computational fluid dynamics-heat transfer problems is introduced. The theory behind the newly proposed technique hereafter named “The Meshless Control Volume Method” is explained and a number of examples illustrating the implementation of the method is presented. In this study, the technique is applied for one and two dimensional transient heat conduction as well as one and two dimensional advection-diffusion problems. Compared to other methods including the exact solution, the results show to be highly accurate for the considered cases. Being a meshless technique, the control volumes are arbitrary chosen, and they posses simple shapes which contrary to the existing control volume methods can overlap. The number of points within each control volume and, therefore the degree of interpolation can be different throughout the considered computational domain. Since the control volumes are of simple shapes, the integrals can be evaluated analytically.

scholarly journals A New Formulation of Maxwell’s Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 868
Author(s):  
Simona Fialová ◽  
František Pochylý
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Control Volume ◽  
Control Volume Method ◽  
Integral Forms ◽  
New Formulation ◽  
Electrical Induction ◽  
Volume Method ◽  
Integral Identities

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

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