A local meshless method for solving multi-dimensional Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems arising in plasma physics

被引：24

作者：

Dehghan, Mehdi ^{[1
]}

Abbaszadeh, Mostafa ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, 424 Hafez Ave, Tehran 15914, Iran

来源：

ENGINEERING WITH COMPUTERS | 2017年 / 33卷 / 04期

关键词：

Meshless methods and finite difference (FD) approach; Local radial basis functions (RBFs); Collocation method; RBFs-FD technique; Reproducing kernel particle method (RKPM); Vlasov-Poisson system; Vlasov-Poisson-Fokker-Planck system; LEAST-SQUARE APPROXIMATION; REPRODUCING KERNEL-METHOD; BOUNDARY NODE METHOD; RBF-FD; NUMERICAL-SOLUTION; PARTICLE METHODS; SHAPE PARAMETER; GALERKIN METHOD; ELEMENT METHOD; SCHEME;

D O I：

10.1007/s00366-017-0509-y

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we use a linear combination of the shape functions of reproducing kernel particle method (RKPM) and RBFs for achieving the unknown weights into each stencil. We obtain an error bound for the new shape function. Also, in this paper, we investigate a numerical procedure based on the presented technique for solving the Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems. The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma. The Vlasov-Poisson equations are used to describe various phenomena in plasma, in particular Landau damping and the distributions in a double layer plasma. We use the RKPM/RBF-FD technique for discretization of space direction and employ the method of lines to achieve a high-order accuracy in temporal direction. Numerical examples are reported which demonstrate the theoretical results and the efficiency of proposed scheme.

引用

页码：961 / 981

页数：21

共 91 条

[1] Highly efficient numerical algorithm based on random trees for accelerating parallel Vlasov-Poisson simulations [J].