Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions

To improve fidelity of nuclear reactor design and safety analyses, the multi-physics neutronics and thermalhydraulics should be solved as a coupled problem. However, coupled, non-linear problems are slow to converge and computationally expensive as they require fine mesh, if solved using conventional schemes. Another challenge is in the verification of any numerical scheme developed to solve highly non-linear problems. Both of these challenges have been addressed in this thesis. Nodal Integral Method (NIM) is a coarse-mesh method. Hence, NIM can achieve the same accuracy as many conventional numerical methods using coarser meshes and less CPU times. Method of Manufactured Solutions (MMS) is used to provide exact analytical solutions for code verification. A nodal integral method (NIM) is developed in this thesis to solve coupled neutron diffusion and heat conduction problems with temperature-dependent thermal conductivity, neutron diffusion coefficient, and cross-sections. A modified nodal integral approach is used for the one-dimensional geometries while ordinary nodal integral scheme is developed for higher dimensions. Method of manufactured solutions is used to provide exact solutions to verify the nodal integral method schemes. Numerical scheme is developed for 1D, 2D, and 3D problems. Numerical results are reported for two problems in 1D, two problems in 2D, and two problems in 3D. Results from the nodal integral method are compared to the exact manufactured solutions and the Root Mean Square (RMS) errors are reported, as well as, the CPU times, and the number of iterations needed to achieve the desired convergence criteria. The spatial order of accuracy of the nodal integral scheme for one-dimensional and multi-dimensional problems is calculated using the RMS errors. In all cases, the schemes are second or near-second order accurate.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Nuclear, Plasma, Radiolgc Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Hegazy, Aya Hamdy

Contributors dc:contributor

• Uddin, Rizwan
• Kozlowski, Tomasz

• NIM
• MMS

Statement dc:rights

• © 2022 Aya Hamdy Hegazy

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115610

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115610