A characteristic mapping method for high resolution simulations of plasma with collisions

We present first results towards simulating kinetic plasmas with collisions using the characteristic mapping method (CMM) [1]. CMM is a semi-Lagrangian method that utilises the semi-group structure of diffeomorphic flows. Here the flow map is decomposed into submaps that relate the flow backward in time to its initial point. This compositional refinement enables exponential resolution within linear time. In addition to [1] we extend CMM to handle source terms by storing sub-integrals corresponding to individual submaps, which facilitates efficient integration. Moreover, it exploits the Lagrangian structure to circumvent implicit time integration in the hydrodynamic regime, which is notoriously stiff. We will demonstrate the effectiveness of the CMM method by benchmarking it using BGK and Vlasov-Poisson-BGK equations.

[1] P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave and K. Schneider. A Characteristic Mapping Method for Vlasov-Poisson with extreme resolution properties. Commun. Comput. Phys., 35(4):905-937, 2024