1. Improved weighted ENO scheme based on parameters involved in nonlinear weights
- Author
-
G. Naga Raju and Samala Rathan
- Subjects
Conservation law ,Applied Mathematics ,Finite difference ,Order of accuracy ,Classification of discontinuities ,01 natural sciences ,010305 fluids & plasmas ,Euler equations ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,Nonlinear system ,Robustness (computer science) ,Norm (mathematics) ,0103 physical sciences ,symbols ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
Here, we have analyzed the weights of the fifth-order finite difference weighted essentially non-oscillatory WENO-P scheme developed by Kim et al. (J. Sci. Comput. 2016) to approximate the solutions of hyperbolic conservation laws. The main ingredient of WENO schemes is the construction of smoothness indicators, which resolves odd behavior of the scheme near discontinuities. In WENO-P, the smoothness indicators are constructed in L 1 โ norm. It is observed that analytically as well as numerically, the WENO-P weights do not achieve required ENO order of accuracy near discontinuities. To recover the desired order of accuracy, we have imposed some constraints on the weight parameters to guarantee that the WENO-P scheme achieves the desired ENO order of accuracy near discontinuities and have the over all fifth-order accuracy in smooth regions of solutions with an arbitrary number of vanishing derivatives. Numerical results are presented with the new weights to verify the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations.
- Published
- 2018