Abstract:
A low dissipative non-oscillatory entropy stable scheme is presented for shallow water equations. The scheme is given to construct entropy stable flux by addition of the entropy viscosity term of entropy conservative flux into Roe's entropy stable flux, to controlling entropy production at discontinuities, which result have enough entropy dissipative to remove oscillations near discontinuity. Further, high resolution entropy stable flux is constructed for the flux limiter functions. These new fluxes is tested on one dimensional and two dimensional problems, numerical examples demonstrate that these schemes are low dissipative,high resolution and non-oscillatory.