A new monotonicity limiter algorithm is presented,particularly suited for unstructured grid applications,so as to constrain the interpolated values on either side of the interface by imposing a monotonicity coefficient on the gradient of each cell.

Adaptive unstructured grids and second-Godunov-type PLM,together with Euler-Lagrange model were used to calculate the gas-particle two-phase flow field under the condition of different particle loading ratio and different particle sizes.

Numerical traits of several Godunov-type schemes are studied.

The Godunov scheme for pressure gradient equations;

The Godunov scheme with an exact Riemann solution is used to solve the shallow water equations, and the classical Riemann solution on dry flat bed is improved to be suitable to the moving boundary with non-flat bed.

Using the Godunov scheme based on the exact Riemann solution with WLF Method, the tidal bore in the Qiantang Estuary is simulated.

Well-balanced Godunov-type scheme for 2D shallow water flow with triangle mesh;

A Godunov-type scheme for 1-D shallow-water flow with uneven bottom;