This presentation introduces the Lagrangian–Eulerian Stabilized Collocation Method (LESCM), a hybrid computational framework combining Lagrangian particle tracking with Eulerian collocation on fixed nodes. LESCM can be used in fluid dynamics, including fluid-structure interaction (FSI), water wave dynamics, and Lagrangian coherent structure analysis of fluid. The method circumvents computationally intensive neighboring-particle searches while maintaining numerical consistency via high order reproducing kernel (RK) approximations. For FSI problems, the method efficiently simulates free surface flows interacting with rigid bodies while preserving mass and momentum conservation. In ocean engineering, LESCM is implemented in a novel numerical wave tank (NWT) to simulate wave generation, propagation, and absorption, providing a reliable tool for offshore wave-structure interaction studies. Beyond flow simulation, LESCM’s Eulerian framework enables precise LCS extraction via finite-time Lyapunov exponents calculated directly on fixed nodes, avoiding errors from particle shifting techniques and accurately resolving critical flow features like vortices. Validated across diverse benchmarks, LESCM demonstrates exceptional efficiency, as it can handle 16 million particles in MATLAB without parallelization, and bridges high-fidelity simulations with real-world engineering demands. By unifying accuracy, efficiency, and adaptability, LESCM emerges as a powerful tool for advancing fluid dynamics simulation and industrial applications.