A coupled Eulerian Lagrangian approach for fluid and particle dynamics

Abstract

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.