Description
CRATOS-MHD is a numerical framework for solving the time-dependent, three-dimensional, compressible, visco-resistive magnetohydrodynamic (VRMHD) equations in the presence of geometrically complex resistive walls. Of specific interest are problems involving fast transient events containing weak solutions which exhibit steep gradients, such as disruptions and vertical displacement events in tokamaks. A combination of second- and higher-order shock-capturing finite volume methods is employed for evolving the hyperbolic part of the equations, and implicit methods for the parabolic terms. The numerical errors resulting from non-zero divergence of the magnetic field are addressed using either a mixed hyperbolic divergence cleaning method, or an adapted form of the constrained transport method, which retains the magnetic solenoidal constraint to machine precision. The deviation well-balancing method is used to eliminate truncation error on initial equilibria, allowing very small amplitude perturbations to be evolved accurately and fully non-linearly, even over long timescales. The governing equations are solved on a single, hierarchically adaptively refined Cartesian computational mesh which spans the plasma vessel as well as the surrounding conducting structures. An embedded boundary method captures the complex, non-grid-aligned geometry of the vessel wall and facilitates two-way non-linear communication across the plasma-solid material interface. This approach can quickly generate high-quality computational meshes from STL files with minimal user input. The hierarchical AMR dynamically tracks steep gradients and other features that warrant locally increased resolution, and adapts the solution in time and space, alleviating the need for field-aligned meshes.
The resulting software package is extensively validated against benchmarks with known exact solutions and case studies from literature, including Riemann problems, vertical displacement events in the presence of ideal and finite-resistivity walls, and pressure-driven edge localised modes. In its current state, the code forms an MHD dynamical core upon which additional physics modules can be added for the simulation of a broad range of nonlinear phenomena.