A non-oscillatory and conservative semi-Lagrangian scheme with fourth-degree polynomial interpolation for solving the Vlasov equation

作者：Umeda Takayuki^*; Nariyuki Yasuhiro; Kariya Daichi

来源：Computer Physics Communications, 2012, 183(5): 1094-1100.

DOI：10.1016/j.cpc.2012.01.011

• Vlasov equation
• Hyperbolic equation
• Numerical interpolation
• Conservative scheme

A conservative semi-Lagrangian scheme for the numerical solution of the Vlasov equation is developed based on the fourth-degree polynomial interpolation. Then, a numerical filter is implemented that preserves positivity and non-oscillatory. The numerical results of both one-dimensional linear advection and two-dimensional Vlasov-Poisson simulations show that the numerical diffusion with the fourth-degree polynomial interpolation is suppressed more than with the cubic polynomial interpolation. It is also found that inherent conservation properties of the Vlasov equation can be improved by combining numerical fluxes of the upwind-biased and central fourth-degree polynomial interpolations.

• 出版日期2012-5