A meshless method for solving a two‐dimensional transient inverse geometric problem

Abstract

Purpose

The purpose of this paper is to apply the meshless method of fundamental solutions (MFS) to the two‐dimensional time‐dependent heat equation in order to locate an unknown internal inclusion.

Design/methodology/approach

The problem is formulated as an inverse geometric problem, using non‐invasive Dirichlet and Neumann exterior boundary data to find the internal boundary using a non‐linear least‐squares minimisation approach. The solver will be tested when locating a variety of internal formations.

Findings

The method implemented was proven to be both stable and reasonably accurate when data were contaminated with random noise.

Research limitations/implications

Owing to limited computational time, spatial resolution of internal boundaries may be lower than some similar case investigations.

Practical implications

This research will have practical implications to the modelling and monitoring of crystalline deposit formations within the nuclear industry, allowing development of future designs.

Originality/value

Similar work has been completed in regards to the steady state heat equation, however to the best of the authors' knowledge no previous work has been completed on a time‐dependent inverse inclusion problem relating to the heat equation, using the MFS. Preliminary results presented here will have value for possible future design and monitoring within the nuclear industry

Citation

Dawson, M., Borman, D., Hammond, R.B., Lesnic, D. and Rhodes, D. (2013), "A meshless method for solving a two‐dimensional transient inverse geometric problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 5, pp. 790-817. https://doi.org/10.1108/HFF-08-2011-0153