This paper gives a comprehensive overview of the popular animation simulation algorithms based on physical and data-driven methods as well as their applications in recent years. Firstly, the traditional physically-based acceleration fluid simulation methods are summarized, covering both their advantages and disadvantages. Then, the existing data-driven algorithms applied in fluid simulation are summarized and analyzed. In particular, the existing data-driven methods are sumed up into three types, namely, interpolation methods, methods based on pre-computed data, and deep learning methods. Further, some key points are given about the data-driven methods as well as the research trends and directions.