Implementation and Verification of Two-fluid Modeling in NIMROD

A second-order time advance for the two-fluid plasma model with equilibrium flow and drift has been developed and implemented in the NIMROD fusion MHD code. The algorithm retains the leapfrog character of the MHD algorithm [JCP 195, p. 355 (2004)] but solves separate implicit advances for each field. Analysis shows that this approach is numerically stable at arbitrarily large time-step when advection and drift terms, including gyroviscosity, are time-centered in each segment of the leapfrog. Implementation relies on Krylov methods with sparse approximate matrices solved directly for preconditioning and with matrix-free computations in the Krylov-space iterations. The implementation is tested on linear wave, interchange, and magnetic reconnection problems where analytic results are readily available.