A Finite Difference Method for the Allen-Cahn Equation in Polar Coordinate System

2021 ◽  
Vol 10 (01) ◽  
pp. 109-114
Author(s):  
俊蓉 霍
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Coordinate System ◽  
Difference Method ◽  
Polar Coordinate System ◽  
Cahn Equation ◽  
Polar Coordinate

scholarly journals Modelling and simulation of heat conduction in 1-D polar spherical coordinates using control volume-based finite difference method

2016 ◽  
Vol 26 (1) ◽  
pp. 2-17 ◽  
Author(s):  
Attila Diószegi ◽  
Éva Diószegi ◽  
Judit Tóth ◽  
József Tamás Svidró
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Coordinate System ◽  
Heat Transport ◽  
Difference Method ◽  
Control Volume ◽  
Polar Coordinate System ◽  
Heat Absorption ◽  
Content Type ◽  
Polar Coordinate

Purpose – The purpose of this paper is to obtain a finite difference method (FDM) solution using control volume for heat transport by conduction and the heat absorption by the enthalpy model in the sand mixture used in casting manufacturing processes. A mixture of sand and different chemicals (binders) is used as moulding materials in the casting processes. The presence of various compounds in the system improve the complexity of the heat transport due to the heat absorption as the binders are decomposing and transformed into gaseous products due to significant heat shock. Design/methodology/approach – The geometrical domain were defined in a 1D polar coordinate system and adapted for numerical simulation according to the control volume-based FDM. The simulation results were validated by comparison to the temperature measurements under laboratory conditions as the sand mould mixture was heated by interacting with a liquid alloy. Findings – Results of validation and simulation methods were about high correspondence, the numerical method presented in this paper is accurate and has significant potential in the simulation of casting processes. Originality/value – Both numerical solution (definition of geometrical domain in 1D polar coordinate system) and verification method presented in this paper are state-of-the-art in their kinds and present high scientific value especially regarding to the topic of numerical modelling of heat flow and foundry technology.

A finite difference method for a conservative Allen–Cahn equation on non-flat surfaces

2017 ◽  
Vol 334 ◽  
pp. 170-181 ◽  
Author(s):  
Junseok Kim ◽  
Darae Jeong ◽  
Seong-Deog Yang ◽  
Yongho Choi
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Flat Surfaces ◽  
Cahn Equation
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