Abstract: The computational precision is important for ALE descriptionin liquid sloshing simulation to calculate the grid velocity. On the free surface,the grid velocity is corrected by using the curvature thereto improve its description precision. Piecewise smooth functions are used tocalculate the grid velocity inside, they are better than a linearrelationship applied before for the subdivision of the high quality grid.A 2D problem excited in a rectangular tank is computed and results are comparedwith experiment, as in the reference. The advantage of using high precisiongrid velocity is obvious.