Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration

Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this paper, we propose an implicitexplicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program. D. Ghosh Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94550 E-mail: [email protected] M. A. Dorf Physics Division, Lawrence Livermore National Laboratory, Livermore, CA, 94550 E-mail: [email protected] M. R. Dorr Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94550 E-mail: [email protected] J. A. F. Hittinger Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94550 E-mail: [email protected] 2 Debojyoti Ghosh et al. time step sizes are constrained by the stiff collisional time scales. We implement semi-implicit additive Runge-Kutta methods in COGENT, a finite-volume gyrokinetic code for mapped, multiblock grids and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.