Method of characteristics - A review with applications to science and nuclear engineering computation

This paper provides the basics of the Method of Characteristics (MOC) in solving partial differential equations (PDEs) to the problems of interests to science and nuclear engineering. The PDEs are widely used in science and engineering to model physical systems and processes. Such equations are often complex, difficult and/or highly impractical to solve analytically. Although several methods exist to approximate solutions for PDEs, employing an approach that is both computationally - resourceful and reliable is crucial in particular to engineering fields of importance to creating reliable and safe designs of the systems involved. This paper introduces and expounds upon the MOC, a method by which PDE solutions are converged quickly and accurately as compared to alternative methods. The MOC theory is described with a few study cases in showing a step-by-step solution for each. Its detailed application to neutron transport, thermal hydraulics and conductivity imaging are presented.