基于求积矩方法的低温等离子体碰撞框架
A low-temperature plasma collisional framework for quadrature-based moment methods
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中文总结 AI 辅助
针对低温碰撞等离子体物理问题，基于求积矩方法建立数学框架，推导弹性与非弹性碰撞反应积分表达式，讨论不同QBMM计算精度，给出数值解，结果表明扩展求积矩方法优势明显，该框架能捕捉低温等离子体基础物理。
中文摘要 AI 辅助
本文为基于求积矩方法（QBMM）的弹性与非弹性碰撞建立了数学框架，并针对由玻尔兹曼方程表示的低温碰撞等离子体物理问题进行了验证。QBMM比直接欧拉求解器计算效率更高，能为玻尔兹曼方程提供无噪声解并捕捉非平衡速度分布函数。通过将速度分布函数视为离散速度横坐标处加权核函数之和实现QBMM的封闭。推导了所有等离子体粒子（电子、离子和中性粒子）在QBMM框架内反应积分的表达式，并推广到由BGK算子表示的弹性碰撞和由玻尔兹曼算子表示的非弹性碰撞（电离和激发）的任意矩阶。讨论了不同QBMM计算反应积分的精度，并给出了具有弹性和非弹性碰撞的多个低温等离子体物理问题的矩模型数值解。结果表明，使用加权连续高斯核之和的扩展求积矩方法在计算反应积分方面最具优势，与文献结果在速度分布函数和积分矩演化方面取得了良好一致，证明了QBMM碰撞框架充分捕捉了低温等离子体的基础物理。
英文摘要
The mathematical framework for elastic and inelastic collisions for quadrature-based moment methods (QBMM) is developed and validated for low-temperature collisional plasma physics problems represented by the Boltzmann equation. QBMM are more computationally expedient than direct Eulerian solvers and are able to provide a noise-free solution to the Boltzmann equation, as well as capture non-equilibrium velocity distribution functions (VDF). Closure for QBMM is provided by considering that the VDF is a sum of weighted kernel functions placed at discrete velocity abscissas. For all plasma particles (electrons, ions, and neutrals), expressions for the reaction integrals within the QBMM framework are derived and generalized to an arbitrary moment order for elastic collisions represented by a BGK operator and inelastic collisions (ionization and excitation) represented by a Boltzmann operator. The accuracy of different QBMM to compute reaction integrals is discussed, and numerical solutions of the moment model are presented for multiple low-temperature plasma physics problems that feature both elastic and inelastic collisions. It is shown that the Extended Quadrature Method of Moments, which uses a sum of weighted continuous Gaussian kernels, is most advantageous to compute reaction integrals. Good agreement with results from the literature is obtained for the evolution of the VDF and integrated moments, thus demonstrating that the QBMM collisional framework adequately captures the underlying physics of low-temperature plasmas.
