Customizing a desired naturalistic fluid simulation result from video to obtain similar artistic effect is significant in practice. But art-directed customizing is challengeable due to the chaotic nature of the physics contained in it, and this still remains to be a difficult task in spite of rapid advancements of computer graphics during the last two decades. This paper focuses on the problem of physically based fluid re-simulation which is foundational to customize desired naturalistic simulation result from video example. In the previous achievements, conventional algorithms primarily recover 3D geometry of fluid surface or obtain the velocity of fluid particles in video. However, to launch new derivative results, just geometry and velocity are not enough, and physically based driven models are promising. We present a novel method that is capable of efficiently recovering physically driven model from an existing video. We advocate a new approach to calculate the velocity and non-normalized surface geometry under the constraints of the appearance and dynamic behavior of the example fluid in multi-scale framework, and use the calculated physical properties quickly to recover the fluid-driven model. In particular, to calculate the surface geometry more accurately, we introduce a scale factor between normalized geometry and non-normalized geometry to acquire a more accurate result. We propose a novel recovery algorithm, in which the particle densities of lattice Boltzmann method can be recovered more accurately from matching fluid advection geometry with the calculated non-normalized geometry. Fluid re-simulations with different types of density can be achieved, including constrained particle density, auto-advection density, and enhanced particle density. We demonstrate our results in several challenging scenarios and provide qualitative evaluation to our method. Some applications based on our approach are also demonstrated in the implementation.