一种保守的隐式求解器用于0D-2V多物种非线性Fokker-Planck碰撞方程
A conservative, implicit solver for 0D-2V multi-species nonlinear Fokker-Planck collision equations
AI总结：
本研究针对多物种非线性0D-2V轴对称FPR碰撞方程提出优化隐式算法，通过引入King函数、采用特定展开方式及后步投影确保守恒与精度，在弱各向异性等离子体问题中表现优越。
摘要：
本研究提出一种优化的隐式算法，专为精确求解多物种非线性0D-2V轴对称Fokker-Planck-Rosenbluth（FPR）碰撞方程而设计，同时保留质量、动量和能量守恒。我们的方法依赖于在球极坐标中使用FPR（FPRS）碰撞算子的非线性Shkarofsky公式。关键创新在于引入名为King的新函数，对角度坐标采用勒让德多项式展开，对速度坐标采用King函数展开。勒让德多项式展开将呈指数收敛，而King方法（一种矩收敛算法）可确保离散形式下的高精度守恒。此外，采用后步流形投影以精确强制碰撞算子的对称性。通过求解各种非平衡构型下的若干典型问题，我们证明了所提算法对弱各向异性等离子体具有高精度和优越性能。
英文摘要：
In this study, we present an optimal implicit algorithm specifically designed to accurately solve the multi-species nonlinear 0D-2V axisymmetric Fokker-Planck-Rosenbluth (FPR) collision equation while preserving mass, momentum, and energy. Our approach relies on the utilization of nonlinear Shkarofsky's formula of FPR (FPRS) collision operator in the spherical-polar coordinate. The key innovation lies in the introduction of a new function named King, with the adoption of the Legendre polynomial expansion for the angular coordinate and King function expansion for the speed coordinate. The Legendre polynomial expansion will converge exponentially and the King method, a moment convergence algorithm, could ensure the conservation with high precision in discrete form. Additionally, post-step projection onto manifolds is employed to exactly enforce symmetries of the collision operators. Through solving several typical problems across various nonequilibrium configurations, we demonstrate the high accuracy and superior performance of the presented algorithm for weakly anisotropic plasmas.
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