Automatic differentiation approach for solving one-dimensional flow and heat transfer problems

Abstract

Traditional reactor system analysis tools are confronted with challenging difficulties in model development, low accuracy, and poor convergence. To solve these problems, the automatic differentiation (AD) method that allows the automatic numerical calculation of derivatives of functions was adopted to develop the reactor system code in this paper. For the simulation of single-phase models, the steady and transient responses were presented to investigate the effects of the spatial and temporal discretization schemes on modeling accuracy and efficiency. Meanwhile, the comparison of convergence performance between the automatic differentiation using operator overloading (ADOO) and the traditional hand-coded method was completed. Further, in the case of two-phase flow problems, the high-order discrete schemes were applied in this code. It was demonstrated that the reactor system code with single-phase and five-equation two-phase flow models, which adopted the high-order discretization and the ADOO method, performed very well for one-dimensional flow and heat transfer problems.