A Conservative Dynamical Low-rank Method for the Vlasov Equation

Dynamical low-rank method has recently arisen as a popular dimension-reduction technique to solve the high dimensional kinetic equations. When it is applied to the Vlasov equation for plasmas, the overall computational cost can be greatly reduced compared to the full 6d simulation. However, the important physical quantities such as mass, momentum and energy are not guaranteed to be conserved in this framework. We propose a conservative dynamical low-rank method based on a novel macro-micro decomposition of the probability density function. Several benchmark tests will be presented to demonstrate the effectiveness of the proposed approach.