Adaptive artificial viscosity entropy stable scheme for hyperbolic conservation laws

The entropy stable conditions may not be met if entropy conservation schemes are used to solve the equations of hyperbolic conservation laws. To achieve entropy stability, the total entropy of a numerical scheme must be dissipative. The frequently-used method is to add a viscosity mechanism to an entropy conservative scheme. By considering the change characteristics of the size of adaptive artificial viscosity in different parts of the computational domain, a new simple entropy stable scheme was proposed by combining the flux of entropy conservation with the corrected flux of adaptive artificial viscosity. According to the adaptivity of adaptive artificial viscosity, this scheme can achieve the overall high resolution without using any limiters but adjusting the viscosity proportional coefficients C. So the computed solution was stable at its discontinuous parts with enough numerical dissipation while maintaining the high order accuracy at smooth parts with very small viscosity. At the end, several numerical examples were performed to analyze the characteristics of the proposed scheme with reference to the numerical results of entropy stable ERoe scheme and high resolution entropy stable EYee scheme.