High-order WENO schemes with variant nonlinear weights for hyperbolic conservation laws

Abstract: In this talk, we present higher order weighted essentially non-oscillatory (WENO) spatial discretization schemes along with the use of TVD/strong stability preserving Runge-Kutta temporial discretization techniques for solving hyperbolic conservation laws. The main ingredient of WENO schemes is the construction of nonlinear weights especially measuring of derivatives information via smoothness indicators. We present variant types of nonlinear weights and the smoothness indicators. With these nonlinear weights, the accuracy of proposed schemes is demonstrated in smooth regions and in presence of critical points by conducting numerical experiments for scalar, one and two-dimensional system of Euler equations.