Efficient diffusion for high order non-oscillatory entropy stable schemes

This paper proposes an efficient approach to construct non-oscillatory entropy stable fluxes (F^) by adding an efficient diffusion term to the entropy conservative fluxes. Computation of proposed diffusion term does not require restrictive and logically expensive sign stability condition on high order reconstruction process or flux sign stability on high order fluxes. The diffusion term is defined as the absolute difference of non-oscillatory (F˘) and entropy conservative fluxes (F˜) multiplied with sign of jump in entropy variable. The amount of diffusion is adjusted using a limiter function without compromising the entropy stability of the resulting scheme which exhibits both high resolution and the non-oscillatory property. The proposed approach is tested on various standard benchmark test problems. Numerical results demonstrate the effectiveness of the method in achieving high resolution entropy stable schemes, Moreover the scheme maintains formal order of accuracy of the lower order flux used in defining the diffusion term.