picFoam is a fully kinetic electrostatic Particle-in-Cell (PIC) solver, including Monte Carlo Collisions (MCC), for non-equilibrium plasma research in the open-source framework of OpenFOAM. The solver’s modular design, based on the same principles used in OpenFOAM, makes it highly flexible, by allowing the user to choose different methods at run time, and extendable, by building upon templated modular classes. The implementation of the PIC method employing the finite volume method, allows it to simulate on arbitrary geometries in one to three dimensions. OpenFOAM’s barycentric particle tracking is used effectively to perform charge and field weighting from the Lagrangian particle based description to the Eulerian field description and backwards without computational expensive particle searching algorithm. picFoam also includes open and general circuit boundary models for the description of real plasma devices.

Program summary

Program Title: picFoam

CPC Library link to program files: http://dx.doi.org/10.17632/bbsm8tjgjy.1

Developer’s repository link: https://github.com/TFDzarm/picFoam

Licensing provisions: GPLv3

Programming language: C++

Nature of problem: The description of equilibrium and non-equilibrium plasma with its complex collective behavior between charged species. As well as their interaction with circuits connected to the boundaries of the plasma. The applications are versatile and lie e.g. in the description of plasma phenomena like discharges in arcjet electric propulsion systems, as well as a general study of plasma phenomena.

Solution method: Implementation of the Particle-in-Cell method with Monte Carlo Collisions [1] in the open-source numerical toolbox OpenFOAM [2]. By this the newly implemented solver gains access to OpenFOAM’s powerful tool sets and an easy to set up simulation case structure. Fields are solved by employing OpenFOAM’s cell-centered finite volume solvers, this allows for the simulation on arbitrary structured meshes. The leapfrog scheme [1] is employed for the integration of the particle’s equation of motion combined with relativistic and non-relativistic integration schemes for Newton’s second law of motion [3]. Monte Carlo Collision methods include models for the collision of electrons and neutral species, considered collision events are elastic collision events and inelastic excitation and ionization events. Additional models include Coulomb collisions and isotropic scattering of neutral species [4]. The solver is able to bind circuit models, include open circuit, ideal voltage and current sources, as well as general purpose circuits with an ideal voltage source and a resistance, an impedance and a capacity in series, to the plasma domain [5].

Additional comments including restrictions and unusual features: The finite volume method is a relatively rarely used method for implementations of the PIC method, here by employing this method we gain the ability to use arbitrary structured meshes in one to three dimensions. OpenFOAM’s barycentric particle tracking is a novel approach for moving the particles through the mesh. With this method we are able to interpolate (weight) the charges efficiently to the mesh without using computational expensive algorithms to locate the particle’s positions beforehand.

References

[1] C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation, Taylor&Francis 2005

[2] H.G. Weller, G. Tabor, H. Jasak and C. Fureby, A Tensorial Approach to Computational Continuum Mechanics Using Object Orientated Techniques, Computers in Physics 1998

[3] J.-L. Vay , Simulation of beams or plasmas crossing at relativistic velocity, Physics of Plasmas 2008

[4] K. Nanbu, Probability theory of electron–molecule, ion–molecule, molecule–molecule, and Coulomb collisions for particle modeling of materials processing plasmas and cases, IEEE Transactions on Plasma Science 2000

[5] J.P. Verboncoeur, M.V. Alves and V. Vahedi, Simultaneous Potential and Circuit Solution for Bounded Plasma Particle Simulation Codes, 1990

中文翻译：

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picFoam：一种基于OpenFOAM的静电粒子内置求解器

picFoam是一种全动态静电粒子内（PIC）求解器，包括蒙特卡洛碰撞（MCC），用于OpenFOAM开源框架中的非平衡等离子体研究。求解器的模块化设计基于OpenFOAM中使用的相同原理，通过允许用户在运行时选择不同的方法，以及通过基于模板化的模块化类进行扩展，使其具有高度的灵活性。使用有限体积方法的PIC方法的实现，使其可以在一到三个维度上模拟任意几何形状。OpenFOAM的重心粒子跟踪可有效地执行电荷和场加权，从基于拉格朗日粒子的描述到欧拉场描述，再向后进行计算，而无需计算昂贵的粒子搜索算法。

计划摘要

节目名称： picFoam

CPC库链接到程序文件： http : //dx.doi.org/10.17632/bbsm8tjgjy.1

开发人员的资料库链接： https : //github.com/TFDzarm/picFoam

许可条款： GPLv3

编程语言： C ++

问题性质：带电物质之间具有复杂的集体行为的平衡和非平衡等离子体的描述。以及它们与连接到等离子体边界的电路的相互作用。该应用程序用途广泛，例如描述等离子现象，例如电弧喷射电推进系统中的放电，以及对等离子现象的一般研究。

解决方法：在开源数值工具箱OpenFOAM [2]中使用Monte Carlo碰撞[1]实现单元内粒子方法。通过这种方式，新实施的求解器可以访问OpenFOAM的强大工具集和易于设置的仿真案例结构。通过使用OpenFOAM的以单元为中心的有限体积求解器来求解场，从而可以在任意结构化网格上进行仿真。跳越方案[1]用于结合牛顿第二运动定律[3]的相对论和非相对论积分方案对质点运动方程进行积分。蒙特卡洛碰撞方法包括电子和中性物质碰撞的模型，认为碰撞事件是弹性碰撞事件以及非弹性激发和电离事件。其他模型包括库仑碰撞和中性物种的各向同性散射[4]。该求解器能够将电路模型（包括开路，理想电压和电流源以及具有理想电压源以及电阻，阻抗和电容串联的通用电路）绑定到等离子域[5]。

包括限制和异常功能在内的其他注释：有限体积方法是PIC方法的一种相对较少使用的方法，在这里，通过使用此方法，我们获得了在1-3维中使用任意结构化网格的能力。OpenFOAM的重心粒子跟踪是一种将粒子移动通过网格的新颖方法。使用这种方法，我们可以将电荷高效地插值（加权）到网格中，而无需使用昂贵的计算算法来预先定位粒子的位置。

参考文献

[1] CK Birdsall和AB Langdon，“通过计算机模拟进行的等离子体物理”，Taylor＆Francis，2005年

[2] HG Weller，G。Tabor，H。Jasak和C. Fureby，使用面向对象技术的计算连续体力学的张量方法，物理计算机，1998年

[3] J.-L. Vay，以相对论速度穿过光束或等离子体的模拟，等离子物理学2008

[4] K. Nanb​​u，《电子-分子，离子-分子，分子-分子和库仑碰撞的概率论，用于处理等离子体和壳体的材料的颗粒建模》，IEEE Transactions on Plasma Science 2000

[5] JP Verboncoeur，MV Alves和V. Vahedi，《有界等离子体粒子模拟代码的同时电势和电路解决方案》，1990年