HIGH ORDER AND ENERGY PRESERVING DISCONTINUOUS GALERKIN METHODS FOR THE VLASOV-POISSON SYSTEM
HIGH ORDER AND ENERGY PRESERVING DISCONTINUOUS GALERKIN METHODS FOR THE VLASOV-POISSON SYSTEM
复制标题
VLASOV-Poisson系统的高阶节能不连续Galerkin方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Soheil Hajian
中科院分区：
文献类型：
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作者：
B. A. Dios;Soheil Hajian
本文对最近在（4）中介绍的一维Vlasov-Poisson方程组的一类间断Galerkin方法进行了计算研究。我们介绍了一个轻微的modication的方法，以允许可行的计算，同时保持原有的方法的属性。我们数值研究了理论验证和收敛性分析，并讨论了格式的守恒性。这些方法通过应用于等离子体物理模拟中的一些基准进行了验证。数值模拟已成为理解等离子体或粒子束在许多情况下的复杂行为的主要工具。这不仅是由于等离子体行为的大量物理应用和技术含义，而且还由于用于描述这种行为的模型的内在二重性。事实上，人们很早就认识到，不存在一个完全令人满意的宏观模型（uid方程）来描述激光聚变问题中的粒子相互作用。相比之下，微观模型（动力学方程）可以提供更准确的描述等离子体。目前在等离子体模拟中使用的最简单的模型问题之一是Vlasov-Poisson系统。该系统描述了带电粒子（电子和离子）等离子体在输运和自洽电场作用下的演化过程。未知量，通常用f（x;v;t）表示（x代表位置，v代表速度，t代表时间），代表粒子（离子，电子等）的分布函数。相空间中。通过泊松方程考虑了与自洽静电场（忽略磁效应）的耦合。系统的非线性结构阻止获得解析解，除了少数学术案例（参见调查（35，13，26）对问题的数学分析的最新技术的良好描述）。因此，必须进行数值模拟来研究现实的物理现象。目前，可以区分两大类用于模拟等离子体的数值方法;拉格朗日（或概率）和欧拉（或确定性）方法。前一类包括所有不同的
We present a computational study for a family of discontinuous Galerkin meth- ods for the one dimensional Vlasov-Poisson system, recently introduced in (4). We introduce a slight modication of the methods to allow for feasible computations while preserving the properties of the original methods. We study numerically the verication of the theoretical and convergence analysis, discussing also the conservation properties of the schemes. The methods are validated through their application to some of the benchmarks in the simulation of plasma physics. Numerical simulation has become a major tool for understanding the complex behavior of a plasma or a particle beam in many situations. This is due not only to the large number of physical applications and technological implications of the behavior of plasmas, but also to the intrinsic diculties of the models used to describe such behavior. In fact, it was recog- nized long time ago that there does not exist any fully satisfactory macroscopic model (uid equations) which can be used to describe the particle interaction in laser-fusion problems. In contrast, microscopic models (kinetic equations) can provide a more accurate description of the plasmas. One of the simplest model problems that is currently used in the simulation of plasmas is the Vlasov-Poisson system. Such system describes the evolution of a plasma of charged particles (electrons and ions) under the eects of the transport and self-consistent electric eld. The unknown, typically denoted by f(x;v;t) (with x standing for position, v for velocity and t for time), represents the distribution function of particles (ions, electrons, etc.) in the phase space. The coupling with a self-consistent electrostatic eld (neglecting magnetic eects) is taken into account through the Poisson equation. The nonlinear structure of the system prevents from obtaining analytical solutions, except for a few academic cases (see the surveys (35, 13, 26) for a good description on the state of the art of the mathematical analysis of the problem). Therefore, numerical simulations have to be performed to study realistic physical phenomena. At the present time, there can be distinguished two main classes of numerical methods for simulating plasmas; Lagrangian (or probabilistic) and Eulerian (or deterministic) methods. The former class include all dierent