In order to ensure conservative precision and monotonicity of a remapping algorithm and discontinuity with high resolution, a new kind of conservative RBF remapping algorithm is developed based on radial based function interpolation. Conservative precision is tested with a conservative error remapping algorithm. Numerical results are obtained for smooth and discontinuous functions. Compared with other remapping methods,the method gives good numerical results.

Riemann problems are constructed at interface in front tracking (FT) method for multi-fluid flows to study application of shock limiter.In gas-gas and gas-water problems,shock limiter parameter is selected about 0.3 considering average conservation error,L₁ error and strength of the shock.It is indicated that in order to obtain better solutions the back shock wave should be selected as an original state for Riemann problems at the interface as a shock is close to a material interface.

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.