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Computational Reactor Physics

Our research is mostly in the area of computational physics and is strongly based on the use of methods from numerical analysis. During our research projects we develop and extend a variety of analysis tools that are partially described below. This list contains brief explanations of the purpose, the capabilities and the numerical techniques employed.

**DALTON**

One of the first tools developed was DALTON which is a multigroup neutron diffusion code. This code was developed to fit our needs to perform coupled calculations involving heat transfer (HEAT) and neutron diffusion. The methodology is through finite volumes and uses standard central approximation for the diffusion term. Time-stepping is supported which is required for physics-coupling.

Application Area: Neutron diffusion, coupled calculations

Special features: Modal calculations (k-eigenvalues, time-eigenvalues)

References

**HEAT**

HEAT is an in-house developed finite volume method tool that solves the incompressible Navier-Stokes equations on structured orthogonal meshes including a heat equation. Classic discretization techniques are used with TVD methods for convection. Time-stepping uses a pressure-correction technique. Krylov solvers are used for the linear systems. HEAT has served an important role in our research in the field of coupled calculations for nuclear reactors such as the HTR and MSR.

HEAT mostly superseded by DG-FLOW.

Application areas: Incompressible Navier-Stokes with heat transfer

Special Features: Previously used in multiphysics coupling for high temperature (HTR) and molten salt reactors (MSR)

References

**DG-FLOW**

This CFD code solves for the Navier-Stokes equations for low-Mach numbers. Conservative variables are used as main variables (momentum, volumetric enthalpy) with the exception of density (replaced by pressure due to the low-Mach numbers). Spatial discretization is based on the discontinuous Galerkin method. A generalized Interior Penalty Method (SIPG) is used for the stress terms and Lax-Friedrichs fluxes are used for convection. The code time steps using a pressure-correction scheme. Linear solvers are called from the PETSc library. The code has RANS capabilities in the form of the k-epsilon and k-omega models. Further, Implicit Large Eddy Simulation (ILES) will be investigated in the near future.

Application areas: Implicit LES, RANS modeling

Special features: Unstructured meshes; Equal order or unequal order approximations, Actively under development

**PHANTOM-SN**

This is an in-house-developed state-of-the-art discrete ordinates code that solves the neutral Boltzmann equation in multigroup form with anisotropic scatter. Discretization is based on the first-order form and uses a discontinuous Galerkin method for the spatial part and is able to use most types of element types (triangles, quadrilaterals, tetrahedra and hexahedra). Time-dependent calculations are supported for use in multi-physics schemes. Solution methods are based on preconditioned Krylov methods with Diffusion Synthetic Acceleration (DSA) as option. The code supports automated spatial refinement (both regular and goal-based).

Application areas: Neutral particle transport (neutrons/photons)

Special features; Time-dependence, Modal calculations (k-eigenvalues and time-eigenvalues)

References

**PHANTOM-DG**

This code extends PHANTOM-SN with the capability of non-SN discretization in angle. In PHANTOM-DG, the sphere of directions is discretized based on discontinuous finite element techniques. The sphere is tessellated using spherical triangles that originate by projecting hierarchically refined triangles on the octahedron onto the sphere surface. The basis functions in angle are discontinuous across the spherical triangles and include a variety of choices: constant, linear on the octahedron (3 unknowns per triangle) or linear in direction (4 unknowns per triangle). Contrary to standard discrete ordinates schemes, this angular discretization is locally refinable on the sphere, thereby focusing efforts in specific regions of angular space. Linear solvers are based on preconditioned Krylov methods. This is especially important for charged particle radiative fields that exhibit highly forward peaked scatter. PHANTOM-DG also includes continuous slowing down based on a discontinuous Galerkin treatment and Fokker-Planck angular diffusion treated by the Interior Penalty Method (SIPG). The code is currently able to refine in space, angle and combined space-angle based on error estimation of the solution.

Application areas: Highly directional radiation and charged particle transport

Special features: Modal calculations possible (k-eigenvalues and time-eigenvalues) through use of the Arpack library

References