Development of a Modified Seventh-Order WENO Scheme with New Nonlinear Weights

The aim of this paper is the presentation of a new modified weighted essentially non-oscillatory scheme with a seventh-order of accuracy, and, a novel nonlinear weighting method. Local smoothness indicators of this scheme constructed using Lagrange’s interpolation polynomial. We developed a new high-order global smoothness indicator, which guarantees the optimal order of accuracy of the scheme at critical points. We used the linear advection equation for verification of the order of accuracy at critical points. Later, we used a series of one- and two-dimensional benchmark problems to verify the shock-capturing capabilities and improved numerical resolution of the new scheme.