Fluid Simulation Analysis of Eulerian, Lagrangian, and Hybrid Approaches for Graphics and CFD Applications

Fluid simulation has emerged as a key area bridging computer graphics and computational fluid dynamics (CFD), enabling realistic simulation of liquids, gases, and reacting phenomena in entertainment, engineering, and scientific applications. This review systematically evaluates three major simulation paradigms—Eulerian mesh-based techniques, Lagrangian particle-centric methods, and hybrid approaches—by analyzing their theoretical foundations, implementation challenges, and performance results. The thesis examines the strengths and weaknesses of Eulerian–Stokes solvers for stable large-scale simulations, Lagrangian smoothed particle hydrodynamics (SPH) for adaptive fluid tracking, and hybrid frameworks such as Fluid Implicit Particle (FLIP) that incorporate mesh-particle duality. Case studies covering filmmaking, disaster scenario modeling, and real-time gaming demonstrate that hybrid approaches can reduce computational costs by up to 40% while maintaining visual and physical fidelity and outperform pure Eulerian or Lagrangian systems in terms of scalability. Emerging trends, including GPU-accelerated solvers, machine learning-enhanced turbulence modeling, and adaptive mesh refinement (AMR), are considered transformative drivers for future developments. The study highlights how interdisciplinary innovations, such as physically-informed neural networks (PINN) and multiresolution coupling, reshape simulation accuracy and efficiency. By synthesizing these insights, this study provides a roadmap for optimizing the next generation of fluid simulation tools, highlighting the need for adaptive hardware-aware algorithms to meet the growing computational demands in industrial and research environments.