AI 中文总结
该研究提出用于模拟二维不可压缩流中流体与粒子动力学的耦合欧拉-拉格朗日计算框架，扩展了GPU加速求解器，通过特定格式积分方程、插值实现耦合，经多种验证，具有计算效率高、扩展性稳定等优势，适用于相关研究。
AI 中文摘要
我们提出了一种单向耦合欧拉-拉格朗日计算框架，用于模拟二维不可压缩流中的流体和粒子动力学。该框架通过纳入被动示踪剂和有限惯性粒子模块扩展了GPU加速的GHD2D傅里叶伪谱纳维-斯托克斯求解器。欧拉流体方程用二阶亚当斯-巴什福斯格式积分，粒子轨迹用经典四阶龙格-库塔方法推进。通过双线性、双三次卡特穆尔-罗姆和双三次B样条格式对流场进行空间和时间插值实现欧拉和拉格朗日描述之间的耦合。该框架通过解析解以及流体求解器、示踪剂输运和惯性粒子动力学的基准问题进行验证。双线性插值产生的输运统计与高阶格式几乎相同，同时具有更高的计算效率，粒子数收敛证明了统计稳健性。对二维衰减湍流中的示踪剂和惯性粒子的模拟捕捉了长时间输运、湍流扩散、涡旋捕获、相干结构相互作用、优先浓度和惯性相关输运。该求解器在保持高效单GPU性能的同时，随网格分辨率和粒子数具有稳定的扩展性。模块化架构和计算效率使该框架适用于湍流输运和含粒子不可压缩流的欧拉-拉格朗日研究。
英文摘要
We present a one-way coupled Eulerian-Lagrangian computational framework for simulating fluid and particle dynamics in two-dimensional incompressible flows. The framework extends the GPU-accelerated GHD2D Fourier pseudospectral Navier-Stokes solver \cite{Mukherjee2018,Biswas2024} by incorporating passive tracer and finite-inertia particle modules. The Eulerian fluid equations are integrated using a second-order Adams-Bashforth scheme, while particle trajectories are advanced with a classical fourth-order Runge-Kutta method. Coupling between the Eulerian and Lagrangian descriptions is achieved through spatial and temporal interpolation of the fluid fields using bilinear, bicubic Catmull-Rom, and bicubic B-spline schemes. The framework is verified using analytical solutions and benchmark problems for the fluid solver, tracer transport, and inertial-particle dynamics. Bilinear interpolation produces transport statistics nearly identical to higher-order schemes while providing greater computational efficiency, and particle-number convergence demonstrates statistical robustness. Simulations of tracer and inertial particles in decaying two-dimensional turbulence capture long-time transport, turbulent dispersion, vortex trapping, coherent-structure interactions, preferential concentration, and inertia-dependent transport. The solver exhibits stable scaling with grid resolution and particle number while maintaining efficient single-GPU performance. The modular architecture and computational efficiency make the framework suitable for Eulerian-Lagrangian studies of turbulent transport and particle-laden incompressible flows.
