CUBENS: A GPU-accelerated high-order solver for wall-bounded flows with non-ideal fluids

We present a massively parallel GPU-accelerated solver for direct numerical simulations of transitional and turbulent flat-plate boundary layers and channel flows involving fluids in non-ideal thermodynamic states. While several high-fidelity solvers are currently available as open source, all of them are restricted to the ideal-gas region. In contrast, the CUBic Equation of state Navier-Stokes solver (CUBENS) can accurately model and simulate the non-ideal thermodynamics of single-phase compressible fluids in the vicinity of the vapor-liquid saturation line or the thermodynamic critical point. By employing high-order finite-difference schemes and convective terms in split, kinetic-energy-, and entropy-preserving form, the solver is numerically stable, and robust with minimal numerical dissipation, enabling it to capture the steep variations of non-ideal thermodynamic properties. For cost-effective high-fidelity simulations, in addition to MPI parallelization, CUBENS is GPU-accelerated using OpenACC directives for computation offloading, and asynchronous GPU-aware MPI for efficient GPU-GPU communication. Moreover, CUBENS is compatible with both NVIDIA and AMD GPU architectures, achieving significant performance results while ensuring energy-efficient simulations. For instance, using 64 NVIDIA A100 GPUs compared to 8192 CPUs at the same computational cost results in a speedup of approximately 130×. In multi-node and multi-GPU configurations ranging from 2 to 128 compute nodes (8 to 512 GPUs), a strong scaling efficiency of around 52% and a weak scaling efficiency of 0.88 with 10243 points per GPU, corresponding to approximately 5 billion degrees of freedom, are achieved. The CUBENS solver is validated against selected cases from the literature, covering transitional to turbulent ideal and non-ideal flows up to the transonic regime. In particular, we demonstrate the solver's suitability and applicability for direct numerical simulations of transitional boundary layers with fluids at supercritical pressure and with buoyancy effects. The development of this high-fidelity solver offers the potential for future fundamental research in non-ideal compressible fluid dynamics.本研究提出一款面向过渡流与湍流平板边界层及槽道流的大规模并行GPU加速直接数值模拟求解器，所涉流体处于非理想热力学状态。当前已有多款开源高保真求解器，但均仅支持理想气体区域内的模拟。与之不同，立方状态方程纳维-斯托克斯求解器（CUBENS）可精准建模并模拟气液饱和线附近或热力学临界点附近的单相可压缩流体非理想热力学特性。该求解器采用高阶有限差分格式，且对流项采用分裂形式、动能守恒与熵守恒形式，具备数值稳定性优异、鲁棒性强且数值耗散极低的特点，可精准捕捉非理想热力学属性的剧烈变化。为实现高性价比的高保真模拟，除支持消息传递接口（Message Passing Interface, MPI）并行外，CUBENS还通过OpenACC指令实现计算卸载的GPU加速，并采用异步GPU感知MPI实现高效的GPU间通信。此外，CUBENS兼容英伟达（NVIDIA）与AMD GPU架构，可在保障模拟节能的同时实现优异性能。例如，在同等计算成本下，使用64块英伟达A100 GPU相较于8192颗CPU可实现约130倍的加速比。在2至128个计算节点（对应8至512块GPU）的多节点多GPU配置中，当每块GPU搭载1024³个网格点（对应约50亿个自由度）时，可实现约52%的强缩放效率与0.88的弱缩放效率。CUBENS求解器已通过文献中的典型算例完成验证，覆盖从过渡流到湍流的理想与非理想流动，最高可达跨音速工况。特别地，本研究验证了该求解器适用于超临界压力流体且考虑浮力效应的过渡边界层直接数值模拟。这款高保真求解器的开发，为未来非理想可压缩流体动力学领域的基础研究提供了重要潜力。

搜集汇总

背景与挑战

背景概述

CUBENS是一个GPU加速的高阶求解器，专门用于模拟非理想流体的壁面流动（如边界层和通道流），支持在饱和线或临界点附近的非理想热力学精确建模。它采用高阶数值格式确保稳定性和低耗散，并通过GPU并行化实现高效计算（如使用64个A100 GPU比8192个CPU快约130倍），适用于从过渡到湍流的直接数值模拟，包括超临界压力等复杂场景。