An improved alternative weighted essentially non-oscillatory scheme for conservation laws

Abstract

In the present study, a fifth-order improved alternative weighted essentially non-oscillatory scheme has been developed for nonlinear hyperbolic conservation laws. We have proposed an improved fifth-order smoothness indicator to design the present scheme. Further, the numerical flux evaluation is based on the reconstruction of primitive variables rather than conservative variables. The third-order TVD Runge-Kutta method has been used for the time advancement of the solution. The computations have been performed for various one, two, and three-dimensional test cases. Numerical results are compared with the exact solution and results with other high-resolution schemes. The proposed scheme resolves the fine-scale structure with a higher resolution. Further, it is computationally efficient, produces less spurious oscillations, and shows better conservation of kinetic energy for 3D Taylor-Green vortex case.