Suitable diffusion for constructing non-oscillatory entropy stable schemes

In this work, amount of suitable diffusion in entropy stable fluxes is explicitly characterized to construct non-oscillatory schemes in total variation diminishing (TVD) sense. Further, high resolution entropy stable TVD fluxes are constructed and a generic TVD-entropy stable region is given for the flux limiter functions. The non-oscillatory TVD property of proposed fluxes does not depend on the choice of entropy functions and different choices for diffusion matrices are proposed for these fluxes. These fluxes are extendable to the system of higher dimension and resulting entropy stable schemes are used to numerically compute the solution for Burgers and shallow water equations in 1D and 2D case. It is also shown numerically that, the use of proposed diffusion matrices in TECNO schemes can significantly suppress the oscillations exhibited by them while applied with other diffusion matrices. Numerical results show that the resulting schemes capture steady shock exactly and produce non-oscillatory solution profile with high resolution.