Use of Scaled Sensitivity Coefficient Relations for Intrinsic Verification of Numerical Codes and Parameter Estimation for Heat Conduction

Abstract

Numerical codes are important in providing solutions to partial differential equations in many areas, such as the heat transfer problem. However, verification of these codes is critical. A methodology is presented in this work as an intrinsic verification method (IVM) to the solution to the partial differential equation. Derivation of the dimensionless form of scaled sensitivity coefficients is presented, and the sum of scaled sensitivity coefficients is used in the dimensionless form to provide a method for verification. Intrinsic verification methodology is demonstrated using examples of heat transfer problems in Cartesian and cylindrical coordinate. The IVM presented here is applicable to analytical as well as numerical solutions to partial differential equations.