A new algorithm for toroidal flow shear in a linearly implicit, local $\delta f$ gyrokinetic code is described. Unlike the current approach followed by a number of codes, it treats flow shear continuously in time. In the linear gyrokinetic equation, time-dependences arising from the presence of flow shear are decomposed in such a way that they can be treated explicitly in time with no stringent constraint on the time step. Flow shear related time dependences in the nonlinear term are taken into account exactly, and time dependences in the quasineutrality equation are interpolated. Test cases validating the continuous-in-time implementation in the code GS2 are presented. Lastly, nonlinear gyrokinetic simulations of a JET discharge illustrate the differences observed in turbulent transport compared with the usual, discrete-in-time approach. The continuous-in-time approach is shown, in some cases, to produce fluxes that converge to a different value than with the discrete approach. The new approach can also lead to substantial computational savings by requiring radially narrower boxes. At fixed box size, the continuous implementation is only modestly slower than the previous, discrete approach.

中文翻译：

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线性隐式局部旋动代码中流动剪切的连续时间方法

一种线性隐式局部环形流剪切的新算法 $\delta f$ 描述了旋动代码。与当前的方法后跟许多代码不同，它在时间上连续地处理流动剪切。在线性陀螺动力学方程中，由于存在流动剪切而产生的时间依赖性被分解为可以及时明确地处理它们，而对时间步长没有严格限制。准确地考虑了非线性项中与流切相关的时间相关性，并且对准中性方程中的时间相关性进行了插值。提供了验证代码 GS2 中的实时连续实现的测试用例。最后，JET 放电的非线性陀螺动力学模拟说明了与通常的时间离散方法相比，在湍流传输中观察到的差异。显示了时间连续方法，在某些情况下，产生收敛到与离散方法不同的值的通量。新方法还可以通过需要径向更窄的框来节省大量的计算量。在固定的盒子大小下，连续实现仅比以前的离散方法慢一点。