A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are (1) the adjoint code is obtained by letting the AD tool Tapenade invert the complete layer of message passing interface (MPI) communications, and (2) the adjoint code integrates time-dependent, non-linear and dissipative (hence physically irreversible) PDEs with an explicit time integration loop running for ca. 10⁶ time steps. The approach relies on using the Adjoinable MPI library to reverse the non-blocking communication patterns in the original code, and by controlling the memory overhead induced by the time-stepping loop with binomial checkpointing. A description of the necessary code modifications is provided along with the validation of the computed derivatives and a performance comparison of the tangent and adjoint codes.

在切线和伴随模式下，都使用算法微分（AD）对计算流体动力学代码进行微分。本方法的两个新颖性是（1）通过使AD工具Tapenade反转消息传递接口（MPI）通信的完整层来获得伴随代码，并且（2）伴随代码集成了时间相关的非线性耗散（因此在物理上不可逆）的PDE，具有明确的时间积分循环，运行时间约为。10 ⁶时间步长。该方法依赖于使用Adjoinable MPI库来反转原始代码中的非阻塞通信模式，以及通过使用二项式检查点控制时间步长循环所引起的内存开销。提供了对必要代码修改的描述，以及对计算出的导数的验证以及正切和伴随代码的性能比较。