The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations
The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations
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发表时间：
1998
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通讯作者：
E. Sonnendrücker;J. Roche;P. Bertrand;A. Ghizzo
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作者：
E. Sonnendrücker;J. Roche;P. Bertrand;A. Ghizzo
动力学方程的数值求解，特别是Vlasov类型方程的数值求解，大部分时间是使用PIC(粒子在胞格中)方法进行的，该方法包括通过遵循方程特征曲线的有限数量的粒子来描述方程的时间演化，与外场和自洽场的相互作用使用网格来求解。另一种方法是直接计算网格上的分布函数，方法是在时间上向后跟踪特征一个时间步长，并使用前一个时间步长的分布函数的网格点值对特征脚部的值进行内插。在这篇报告中，我们介绍了最后一种方法及其在不同类型的Vlasov方程中的应用。
The numerical resolution of kinetic equations and in particular of Vlasov type equations is most of the time performed using PIC (Particle In Cell) methods which consist in describing the time evolution of the equation through a finite number of particles which follow the characteristic curves of the equation, the interaction with the external and self consistent fields being resolved using a grid. Another approach consists in computing directly the distribution function on a grid by following the characteristics backward in time for one time step and interpolating the value at the feet of the characteristics using the grid points values of the distribution function at the previous time step. In this report we introduce this last method and its use for different types of Vlasov equations.