## 2 Materials and Methods  
### GeN-Foam Theory and Modeling  
GeN-Foam is built on three sub-solvers that account for three different physics: neutronics, thermal hydraulics, and thermal mechanics. The thermal-hydraulics sub-solver is based on the Pressure-Implicit with Splitting of Operators Semi-Implicit Method for Pressure-Linked Equations (PIMPLE) OpenFOAM solver (buoyantPimplefoam)and the code iterates on the conservation equations first. A thermal-mechanics sub-solver is used to deform and move the mesh if thermal mechanics is active [3]. Finally, these sub-solvers provide results to the neutronics sub-solver which can use the multi-group neutron diffusion equation [11] or SP3 equations [12]. The thermal-hydraulics and neutronics solvers both used the same mesh. The cells of the mesh are tetrahedral and the average cell size outside of the boundary layers is approximately 6 mm.  
The GeN-Foam neutronics solver requires multi-group constants for simulation. Group constants were generated in Serpent 2.1.32 [13] for a six-group structure shown in Table 1[14]. Ten thousand active cycles following twenty inactive cycles were simulated with one million particles each. The Serpent simulations used the Joint-Evaluated Fission and Fusion (JEFF) v3.1.1 nuclear data libraries [15]. All neutronic boundaries in both Serpent and GeN-Foam were vacuums.  
The fuel-salt composition is given by Table 2 with a chemical form of 1 \(\cdot\) PuCl3 8 \(\cdot\) UCl3 10 \(\cdot\) NaCl, yielding a molar weight of 3660 g/mol.  
The GeN-Foam thermal-hydraulics sub-solver requires fluid properties for the simulated domain. Table 3 lists the fluid properties used for this work, which were considered constant and adopted from [PERSON] (2018).  
The geometry and thermal-hydraulic boundary conditions of the LFMSR GeN-Foam model are shown in Figure 2. This initial design has a height of 3.24 m and a radius of 1.25 m. The two-dimensional domain in Figure 2 is only a partial slice of the full LFMSR design to save computational cost. The full LFMSR core design consists of sixteen loops, with each loop consisting of three main components: the core, the pump, and the heat exchanger. The boundary conditions in Figure 2 mimic the full LFMSR core since the entire core contains a single fluid volume in a loop configuration. This model represents a full 1/16 slice of the plant's primary loop.  
All three sub-solvers in GeN-Foam use the finite volume method for discretization of the partial differential equations and can iterate on both structured and unstructured meshes. A backward Euler scheme is used for time-dependent solutions and is the only option available in GeN-Foam. Only neutronics and thermal hydraulics are activated in this work.  
\begin{table}
\begin{tabular}{c c} \hline
**Energy Group** & **Upper Energy Boundary (MeV)** \\ \hline
1 & \(1.500\times 10^{1}\) \\
2 & \(2.231\times 10^{0}\) \\
3 & \(4.979\times 10^{-1}\) \\
4 & \(2.479\times 10^{-2}\) \\
5 & \(5.531\times 10^{-3}\) \\
6 & \(7.485\times 10^{-4}\) \\ \hline \end{tabular}
\end{table}
Table 1: Energy group structure for group constant generation in Serpent 2.1.32.  
\begin{table}
\begin{tabular}{c c} \hline
**Isotope** & **Atomic Fraction** \\ \hline U-235 & \(1.02\times 10^{-3}\) \\ U-238 & \(1.41\times 10^{-1}\) \\ Pu-239 & \(1.33\times 10^{-2}\) \\ Pu-240 & \(1.78\times 10^{-3}\) \\ Pu-241 & \(8.92\times 10^{-4}\) \\ Pu-242 & \(1.78\times 10^{-3}\) \\ Na-23 & \(1.81\times 10^{-1}\) \\ Cl-37 & \(6.59\times 10^{-1}\) \\ \hline \end{tabular}
\end{table}
Table 2: Initial salt composition.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Units** \\ \hline Density & \(4.20\times 10^{3}\) & kg/m\({}^{3}\) \\ Specific Heat Capacity & \(9.50\times 10^{2}\) & J/kg-K \\ Dynamic Viscosity & \(2.17\times 10^{-3}\) & kg/m-s \\ Thermal Expansion & \(4.60\times 10^{-4}\) & 1/K \\ Coefficient & \(7.00\times 10^{-1}\) & W/m-K \\ Prandtl Number & \(2.9450\) & - \\ \hline \end{tabular}
\end{table}
Table 3: Molten-salt properties at 750 K.