Title: Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator Show Chinese title

Title: 轴对称吉罗动力学模拟使用保守隐式BGK碰撞算子的ASDEX-升级边缘层

Abstract: Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar-Gross-Krook (BGK) collision operator for use in the discontinuous Galerkin (DG) full-f gyrokinetic solver within the Gkeyll framework, which, when combined with Gkeyll's traditional explicit time integrator for collisionless advection, can significantly increase the time step in gyrokinetic simulations of highly collisional regimes. To ensure conservation of density, momentum, and energy, we utilize an iterative scheme to correct the discretized approximation to the equilibrium Maxwellian distribution to which the BGK collision operator relaxes. We have further generalized the BGK infrastructure, both the implicit scheme and the correction routine, to handle cross species collisions. This improved implicit and conservative BGK operator is benchmarked against the more accurate but more computationally expensive Lenard-Bernstein-Dougherty (LBD) operator which has been utilized in prior studies with Gkeyll. The implicit BGK operator enables 2D axisymmetric simulations of the ASDEX-Upgrade scrape-off layer to run 56 times faster to completion than the simulations with the LBD operator, because the BGK operator is more robust and converges at a lower resolution than is required by the LBD operator. Additionally, in this more collisional limit, we demonstrate that the results of our simulations utilizing the implicit BGK operator agreed well with simulations utilizing the more computationally expensive LBD operator. Show Chinese abstract

Abstract: 碰撞在聚变等离子体的湍流和输运中起着重要作用。 对于动能模拟，随着感兴趣区域内的碰撞性增加，为了解析碰撞物理而需要的时间步长可能在显式时间积分方案中变得过于严格，导致计算成本高昂。 为了克服这种限制，我们在Gkeyll框架内的不连续伽辽金（DG）全-f回旋动力学求解器中实现了隐式Bhatnagar-Gross-Krook（BGK）碰撞算子，当与Gkeyll传统的无碰撞对流显式时间积分器结合使用时，可以显著增加高碰撞区域的回旋动力学模拟时间步长。 为了确保密度、动量和能量的守恒，我们采用迭代方案来校正离散化的平衡麦克斯韦分布近似值，BGK碰撞算子会趋向于该分布。 我们进一步将BGK基础设施（包括隐式方案和校正过程）推广以处理跨物种碰撞。 这种改进的隐式且守恒的BGK算子与更精确但计算成本更高的Lenard-Bernstein-Dougherty（LBD）算子进行了基准测试，该算子已在之前的Gkeyll研究中被使用。 隐式BGK算子使ASDEX-Upgrade边缘层的二维轴对称模拟比使用LBD算子的模拟快56倍完成，因为BGK算子更稳健，并且在比LBD算子所需更低的分辨率下就能收敛。 此外，在这个更高碰撞极限下，我们证明了使用隐式BGK算子进行的模拟结果与使用计算成本更高的LBD算子进行的模拟结果相符。