A charge-momentum-energy-conserving 1D3V hybrid Lagrangian–Eulerian method for Vlasov–Maxwell system

Abstract

Here we propose hybrid Lagrangian–Eulerian (HLE) method for kinetic simulations of plasmas. The HLE method solves advection equations of shape functions unlike particle-in-cell (PIC) method. Although the PIC method cannot preserve the conservation laws of momentum and energy simultaneously, the HLE method can resolve this issue while the particle velocity is formulated by the Lagrangian description. The HLE method discretizes the advection equations and Maxwell's equations with the same scheme, so the momentum and energy exchange between charged particles and electromagnetic field exactly balances in discrete level. Numerical experiments show that linear growth rates of two-stream and Weibel instabilities are reproduced well, and global conservation is exactly preserved except for round-off errors although the velocity space is discretized by the Lagrangian description like the PIC method.