Multi-Moment Advection scheme for Vlasov simulations

TL;DR

This paper introduces a novel multi-moment advection scheme for Vlasov simulations that improves accuracy and reduces numerical diffusion, especially in modeling plasma phenomena like shock waves.

Contribution

The paper develops a new multi-moment advection scheme that advances point values and moments simultaneously, enhancing Vlasov simulation accuracy.

Findings

Accurate solutions with the same memory as existing schemes

Effective in solving solid body rotation of Gaussian profiles

Successfully applied to electromagnetic Vlasov simulations of shock waves

Abstract

We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. We have developed one- and two-dimensional schemes and show that they provide quite accurate solutions compared to other existing schemes with the same memory usage. The two-dimensional scheme can solve the solid body rotation problem of a gaussian profile with little numerical diffusion. This is a very important property for Vlasov simulations of magnetized plasma. The application of the scheme to the electromagnetic Vlasov simulation of collisionless shock waves is presented as a benchmark test.