Acceleration strategies based on bubble-type adaptive mesh refinement method

Although the adaptive mesh refinement method based on bubble placement can generate a high-quality mesh, the efficiency of bubble placement method remains to be improved. In this study several acceleration strategies are proposed to reduce the cost of simulation. The specific strategies are given as follows: in order to reduce the number of simulation rounds, the bubbles at the new refinement level are added in advance according to the estimated bubble distribution; multilevel time step is adopted for time integration and the time step is defined separately for moving bubbles and oscillating bubbles; a scheme for setting cell length adaptively is proposed and the cell searching method is modified to improve the efficiency of establishing adjacent list; efficiency of updating bubble size is also enhanced by promoting the localization process. Numerical examples illustrate that the computing cost can significantly decrease by 70% via adopting the strategies above, while keeping the mesh quality unchanged compared with the traditional method. It shows that those strategies are efficient and suitable for adaptive mesh refinement.