In this paper, we present a new numerical method for advection in fluid simulation. The method is built on the Characteristic Mapping method. Advection is solved via grid mapping function. The mapping function is maintained with higher order accuracy BFECC method and dynamically reset to identity mapping whenever an error criterion is met. Dealing with mapping function in such a way results in a more accurate mapping function and more details can be captured easily with this mapping function. Our error criterion also allows one to control the level of details of fluid simulation by simply adjusting one parameter. Details of implementation of our method are discussed and we present several techniques for improving its efficiency. Both quantitative and visual experiments were performed to test our method. The results show that our method brings significant improvement in accuracy and is efficient in capturing fluid details. © 2014 Springer-Verlag Berlin Heidelberg.