An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

Vlasov solvers that operate on a phase‐space grid are highly accurate but also numerically demanding. Coarse velocity space resolutions, which are largely unproblematic in particle‐in‐cell (PIC) simulations, can lead to numerical heating or oscillations in continuum Vlasov methods. To address this issue, we present a new dual Vlasov solver which is based on an established positivity preserving advection scheme for the update of the distribution function and an energy conserving partial differential equation solver for the kinetic update of mean velocity and temperature. The solvers work together via moment fitting during which the maximum entropy part of the distribution function is replaced by the solution from the partial differential equation solver. This numerical scheme makes continuum Vlasov methods competitive with PIC methods concerning computational cost and enables us to model large scale reconnection in Earth's magnetosphere with a fully kinetic continuum method. The simulation results agree well with measurements by the MMS spacecraft.

Key Points: A moment fitting continuum Vlasov solver is presented that preserves positivity of the distribution function and conserves total energy.

The method behaves well at low velocity space resolutions, making it competitive with PIC methods concerning computational cost.

There is good agreement of the simulations with measurements of magnetic reconnection by the MMS spacecraft.