A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

中文翻译：

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陀螺平均 Dougherty 碰撞算子的保守不连续 Galerkin 方案

提出了全 f 长波长陀螺动力学中非线性 Dougherty 碰撞算子的保守不连续 Galerkin 方案。从解析上讲，该模型算子具有福克-普朗克算子的平流扩散形式，具有不递减的熵泛函，并且守恒粒子、动量和能量。离散地，这些保守属性也完全保持不变，与数值分辨率无关。在这项工作中，相空间离散化是使用不连续 Galerkin 方案的新版本执行的，使用弱相等和恢复的概念精心构建。离散时间推进是使用显式时间步进算法进行的，我们探索其稳定性限制。