We propose a two-dimensional(2D) monotonicity-and conservation-preserving interpolation operator based on a one-dimensional monotonicity-and conservation-preserving interpolation operator.With several numerical examples we conclude that our interpolation operator is effective.Furthermore,we take it as a refinement interpolation operator in a structured adaptive mesh refinement(SAMR) algorithm to solve numerical examples governed by 2D Euler equation.Results show that our method is effective in SAMR.

We propose a monotonicity- and conservation-preserving interpolation operator, named PQIM. Its order of convergence, conservation-preserving and monotonicity-preserving properties are demonstrated. The interpolation operator is proved to restrain oscillation caused by interpolation effectively.