The Method of Fundamental Solutions for the Moving Boundary Problem of the One-Dimension Heat Conduction Equation

Abstract

The melting of the material is regarded as the moving boundary problem of the heat conduction equation. In this paper, the method of fundamental solution is extended into this kind of problem. The temperature function was expressed as a linear combination of fundamental solutions which satisfied the governing equation and the initial condition. The coefficients were gained by use of boundary condition. When the metal wire was melting, process of the moving boundary was gained through the conversation of energy and the Prediction-Correlation Method. A example was given. The numerical solutions agree well with the exact solutions. In another example, numerical solutions of the temperature distribution of the metal wire were obtained while one end was heated and melting.

Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions

“…Extension of the current work to unsteady flows and coupling to liquid dynamics (Rana et al 2019;Chubynsky et al 2020) can be considered in the future, the liquid phase can be modelled as an incompressible fluid (Stokeset/Oseenlet and heatlet) and the vapour phase modelled via the CCR model. However, it will require solving the moving-boundary problem efficiently within the MFS framework (Jiang et al 2014). Another line of inquiry would be to implement these fundamental solutions via boundary integral methods which offer more flexibility and robustness as compared to the MFS.…”

Efficient simulation of non-classical liquid-vapour phase-transition flows: a method of fundamental solutions

“…Extension of the current work to unsteady flows and coupling to liquid dynamics (Rana et al 2019;Chubynsky et al 2020) can be considered in future-the liquid phase can be modelled as an incompressible fluid (Stokeset/Oseenlet and heatlet) and the vapor phase modelled via CCR model. However, it will require solving the moving boundary problem efficiently within the MFS framework (Jiang et al 2014). Another line of inquiry would be to implement these fundamental solutions via boundary integral methods which offer more flexibility and robustness as compared to the MFS.…”

Numerical Simulations Based on a Meshfree Method for Nickel-Steel Welded Joint Manufactured by Micro-Jet Cooling

“…This version of MFS (with the source point placed in the considered region) is also a perfect tool for solving transient issues. Moreover, the method of the fundamental solution was extended to the condition of moving boundaries [ 32 ]. The proposed innovation of MFS was implemented to solve the problem of melting the material.…”