AI 中文总结
本研究解决量子启发CFD仅适用于不可压缩流动的问题，开发首个基于TT格式的QICFD求解器，通过TGV测试验证其正确性，可并行模拟且成本低，同时指出其需改进以适配工业场景。
AI 中文摘要
量子启发算法是一类新兴的计算流体动力学（CFD）算法，与经典方法相比，其在解决大规模问题时具有潜在的良好扩展性。然而，由于算术限制，它们的应用仅限于不可压缩流动，本研究解决了这一问题。本研究引入了首个完整的量子启发计算流体动力学（QICFD）求解器，用于可压缩纳维-斯托克斯方程的直接数值模拟，即所有算术运算均以张量列车（TT）格式进行。重要的是，新的基于TT的除法和平方根算法使得能够使用用于粘度的萨瑟兰定律（Sutherland's law）。通过与经典CFD求解器HiPSTAR对比，并采用具有挑战性的流体流动测试案例——马赫数为0.8和0.1的低分辨率泰勒-格林涡（TGV）来验证新的QICFD求解器。TGV测试案例是一种瞬态湍流案例，对累积误差非常敏感，但我们的QICFD求解器与经典CFD参考结果达到了极好的一致性。本研究证明了新的TT除法和平方根算法的正确性，且QICFD能够进行可压缩流动模拟。新的QICFD求解器还能够执行并行模拟，以仅10%-20%的额外成本并行运行多个初始化不同的类TGV案例。最后，所展示的TGV测试案例揭示了QICFD的额外挑战，并强调需要未来的进展以使TT方法适用于工业相关条件。
英文摘要
Quantum-inspired algorithms are an emerging class of algorithms for computational fluid dynamics (CFD) with potentially favourable scaling for large problems compared to classical methods. However, their applications have been limited to incompressible flows due to arithmetic limitations, which are addressed in this work. This work introduces the first true end-to-end quantum-inspired computational fluid dynamics (QICFD) solver for direct numerical simulation of the compressible Navier-Stokes equations, that is, all arithmetic operations, as well as initialisation and post-processing, are undertaken in the tensor train (TT) format. Importantly, new division and square-root algorithms using TTs enable the use of Sutherland's law for viscosity, and leverages recent improvements in TT arithmetic algorithms for reduced runtime and memory cost. The new QICFD solver is validated by comparison with the classical CFD solver HiPSTAR and by way of a challenging fluid-flow test case, the low resolution Taylor-Green Vortex (TGV) at Mach numbers of 0.8 and 0.1. The TGV test case is a transient turbulent case that is very sensitive to accumulating errors, yet our QICFD solver achieves excellent agreement with the classical CFD reference. This work demonstrates the correctness of the new TT division and square-root algorithms, and that QICFD is capable of compressible flow simulations. The new QICFD solver is also able to perform simultaneous simulations, running multiple TGV-like cases initialised differently in parallel with reduced extra cost. Finally, the demonstrated TGV test case reveals additional challenges of QICFD as well as highlight the need for future advances to make TT methods viable for industrially-relevant conditions.
Comments19 pages, 6 figures. Added summary figure, expanded simultaneous simulations to four cases
