Skip to main content

Joshua Hodson

Joshua  Hodson

Mechanical & Aerospace Engineering

PhD Student

Contact Information


Development of a Dual Number Automatic Differentiation (DNAD) module for nuclear reactor thermal/hydraulic sensitivity studies. Major Professor:  Robert Spall


Traditional sensitivity studies use Monte Carlo simulations to approximate the relationships between design parameters and system characteristics.  While this approach is sufficient for many applications, it tends to be cost-prohibitive when considering complex systems such as nuclear reactor thermal/hydraulic systems.  Alternative approaches (e.g. adjoint methods and complex step derivatives) have been developed that address some of the shortcomings of the traditional Monte Carlo approach, but applying them to numerical algorithms requires extensive source code modification. Dual Number Automatic Differentiation (DNAD) is a method of performing numerical sensitivity studies through the application of advanced programming concepts.  Automatic differentiation is a method of computing function derivatives based on the elementary mathematical operations used to numerically evaluate the function itself.  Applying DNAD to sensitivity studies has the potential to improve the speed and accuracy of the analysis when compared to the traditional Monte Carlo approach, while requiring significantly less source code modification than the alternatives mentioned earlier.

My research is focused on the development and validation of a C++ DNAD module that can be used within existing and future analysis tools.  For the validation effort, I will develop a CFD code for modeling strongly-heated forced-convection pipe flow representative of the experimental setup studied by Shehata and McEligot (See INEL-95/0223, Nov. 1995).  The DNAD module will then be used to examine the sensitivity of turbulence model coefficients for this test case.  Other validation codes will be identified as necessary to fully validate the DNAD module for nuclear reactor thermal/hydraulic applications.

While the focus for my research will be nuclear reactor thermal/hydraulic analysis software, success here can lead to future work extending the module to other types of numerical analysis.

This research is being funded through a Department of Energy (DOE) Nuclear Energy University Program (NEUP) Fellowship.