Methods for Approximating Discontinuous or Rapidly Changing Conductivity in Numerical Calculations.

"Numerical methods for dealing with a temperature dependent conductivity are discussed. An approach based on a local application of a Kirchhoff transformation at the discrete level is presented. The application of this transformation - that does not require any inversion- is demonstrated on solving a two-dimensional test problem.IntroductionMuch is said in the recent literature on the modeling necessity of obtaining appropriate thermo-physical properties; in particular the requirement to account for properties that are ""strong"" functions of the depended variables, e.g., Temperature. Of course obtaining appropriate thermo-physical properties serves no purpose unless they can be accurately integrated into a discrete numerical calculation. The purpose of this paper is to examine how temperature dependent conductivities that exhibit discontinuities or rapid changes can be handled in a numerical code.The discussion will be made in the context of a control volume finite element method [1]. After a brief outline of control volume finite element fundamentals basic methods of dealing with discontinuous or rapidly changing thermal conductivity are discussed. This is followed by the presentation of the recently proposed local Kirchhoff method [2,3], The paper concludes with an investigation of the performance of the various conductivity schemes in solving two dimensional problems. This testing clearly shows the advantages (accuracy and implementation) in using the local Kirchhoff method."