A new global smoothness indicator of fifth order weighted non-oscillatory scheme for hyperbolic conservation laws

In this work we introduce fifth-order weighted essentially non-oscillatory (WENO) scheme using new global smoothness indicator which demonstrates improved numerical results compared to the solutions obtained using the fifth order WENO-JS schemes. The proposed scheme achieves an optimal level of approximation, even at critical points where both the first and second derivatives vanishes, but not the third derivative. Numerical examples are presented in the subsequent section to check the robustness and accuracy of the proposed scheme for one and two-dimensional systems of hyperbolic equations.