We summarize conservative remapping algorithms based on ENO (essentially non-oscillatory) interpolation. Three numerical techniques in computational fluid dynamics are discussed:overlapping mesh method, adaptive refinement mesh method and moving mesh method. Physical quantities transfer between meshes. Conservativeness is important, especially in computing shock and contact discontinuity. We propose a remapping algorithm based on ENO which is conservative and accurate in transferring physical quantities between meshes and give numerical examples. It shows that the algorithm has ability of resolving conservative problems with above mesh techniques in computational fluid dynamics.

A finite volume scheme is developed for Lagrangian equations in hydrodynamics.With ENO(essentially non-oscillatory) interpolating polynomials on structure grids,a high accurate finite volume scheme is constructed by modifying a first order finite volume scheme on rectangular meshes.Numerical experiments are made with an adaptive moving mesh and arbitrary Lagrangian-Eulerian method.It shows effectiveness of the method.