Accurate monotonicity-preserving schemes with Runge-Kutta time stepping (Q1368168)

The authors introduce a new kind of numerical schemes, designed for both monoticity and accuracy properties. These schemes involve piecewise polynomial solutions, together with an accurate interface formula and Runge-Kutta time stepping. They are presented in details concerning the advection equation with constant speed. In this case, they are proved to be monoticity preserving as well as high-order accurate. Then they are extended to the Euler equations in 1-D and 2-D. Several numerical experiments are provided, in which they compare favorably with ENO and weighted ENO schemes.