A Formal Verification and Validation of a Low Magnetic Reynolds Number MHD Code for Fusion Applications

As the nuclear fusion research advances, researchers and engineers focus more on the design of the required systems that complement the nuclear fusion reaction in the plasma of a Tokamak. Some proposals for breeding blankets as well as plasma-facing components' protection systems are based in liquid metal flows under the Tokamak intense magnetic fields. This creates the situation where induced magnetic field can be neglected and the low magnetic Reynolds number (Re) electric potential formulation can be used to close the magnetohydrodynamic (MHD) system of equations. In the last few years, many different laboratories have developed their own MHD codes to study the liquid metal flow. A formal verification and validation of such codes is necessary to enhance the reliability of the numerical results and to make sure that design decisions are based on safe grounds. The fusion community has made the effort of proposing standardized benchmark cases through which any MHD code should demonstrate its reliability. This work contains the formal validation and verification activities of the MHD code developed some years ago in the Universitat Politecnica de Catalunya (UPC) and currently candidate to contribute to the research done at the Princeton Plasma Phyisics Laboratory (PPPL). The code is implemented over OpenFOAM which makes it easily modifiable. Among these benchmark cases, there are high Hartmann number (Ha), 3-D flows, and magneto-convective interaction cases.