Ben Whewell AI/ML Scientist Santa Fe, NM

Research

Solution verification for transport solvers

Solution verification estimates how much of the error in a simulation comes from the discretization. The usual way to do it is a grid refinement study, which solves the same problem on several successively finer meshes. For large transport problems, the finest of those meshes can be too expensive to run.

Approach

I use the method of nearby problems (MNP), which only needs one spatial grid. An analytical curve fit is interpolated from the numerical solution, and the residual between the curve fit and the numerical solution is added to the governing equation as an extra source term. The nearby problem is then solved with that source and with boundary conditions that match the curve fit. Comparing the nearby solution to the curve fit gives an estimate of the spatial discretization error.

Results

The method finds spatial error in one- and two-dimensional discrete ordinates problems, for both fixed-source and criticality calculations. For the C5G7 benchmark it identifies the regions with high spatial error. The journal paper also combines Monte Carlo with the discrete ordinates nearby problem for one- and two-dimensional fixed-source problems.

Publications

  • Single Grid Error Estimation for Neutron Transport Solvers. Ben Whewell and Ryan G. McClarren, (2025). Journal of Verification, Validation and Uncertainty Quantification. 10(2): 021001. DOI: 10.1115/1.4069426
  • Single Grid Error Estimate in Two-Dimensional Neutron Transport Problems. Ben Whewell and Ryan G. McClarren, (2025). The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering.
  • Solution Verification with the Method of Nearby Problems for Neutron Transport Applications. Ben Whewell and Ryan G. McClarren, (2023). The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering.
  • Hybrid Numerical Methods and Solution Verification for the Neutron Transport Equation. Benjamin Joseph Whewell, (2024). University of Notre Dame. Dissertation. DOI: 10.7274/27927858.v1

Code

The method of nearby problems is part of the verification suite in ants.