The Method of Rotated Solutions: A Highly Efficient Procedure for Code Verification

Abstract

Code verification provides mathematical evidence that the source code of a scientific computing software platform is free of bugs and that the numerical algorithms are consistent. The most stringent form of code verification requires the user to demonstrate agreement between the formal and observed orders of accuracy. The observed order is based on a determination of the discretization error, and therefore requires the existence of an analytical solution. One drawback of analytical solutions based on traditional engineering problems is that most derivatives appearing in the related governing equations (or mathematical model) are identically zero, which limits their scope during code verification. The method of rotated solutions (MRS) is introduced herein as a methodology that utilizes coordinate transformations to generate additional nonzero derivatives in the governing equations and numerical solutions. These transformations extend the utility of even the simplest one-dimensional solutions to be able to perform more thorough evaluations. This paper outlines the rotated solutions methodology and provides an example that demonstrates and confirms the usefulness of this new technique.