Convergence of Roberts flow dynamos in Eulerian and Lagrangian codes
Standard benchmark tests for numerical magnetohydrodynamics codes focus on one- and two-dimensional problems that ignore the possibility of dynamos, i.e., an exponential instability converting kinetic energy into magnetic energy. They also tend to ignore magnetic helicity conservation that can have dramatic effects in periodic domains. The existence of magnetic diffusion is crucial for dynamos, as was exemplified by the impossi- bility of finding dynamo solutions when using Euler potentials, whi…