Improved Seventh-Order WENO Scheme
نویسندگان
چکیده
In this paper, an improved seventh-order WENO (WENO-Z7) scheme is suggested by extending the 5th-order WENO scheme of Borges et al[R. Borges, M. Carmona, B. Costa, W. S. Don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys. 227(2008) 3191-3211]. The sufficient condition for seventh-order accuracy is described for the new smoothness indicator. The role of the parameter ε, which is used to construct the weights of WENO schemes to prevent the denominator from being zero, is discussed, and an optimized value of ε is suggested to improve the convergence and accuracy for practical applications.
منابع مشابه
An efficient class of WENO schemes with adaptive order
Finite difference WENO schemes have established themselves as very worthy performers for entire classes of applications that involve hyperbolic conservation laws. In this paper we report on two major advances that make finite difference WENO schemes more efficient. The first advance consists of realizing that WENO schemes require us to carry out stencil operations very efficiently. In this pape...
متن کاملAn improved WENO scheme with a new smoothness indicator
We present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions. The proposed WENO scheme provides at least the same or improved behavior over the classical fifth-order WENO scheme [9] and other fifth-order ...
متن کاملOptimized Weighted Essentially NonoscillatorySchemes for Linear Waves with Discontinuity
ENO (essentially nonoscillatory) and weighted ENO (WENO) schemes were designed for high resolution of discontinuities, such as shock waves, while optimized schemes such as the DRP (dispersion–relation–preserving) schemes were optimized for short waves (with respect to the grid spacing 1x , e.g., waves that are 6–81x in wavelength) in the wavenumber space. In this paper, we seek to unite the adv...
متن کاملAn improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
We develop in this article an improved version of the fifth-order weighted essentially non-oscillatory (WENO) scheme. Through the novel use of higher order information already present in the framework of the classical scheme, new smoothness indicators are devised and we obtain a new WENO scheme with less dissipation than the classical WENO of Jiang and Shu [2], with the same computational cost,...
متن کاملA conservative high order semi-Lagrangian WENO method for the Vlasov equation
Jing-Mei Qiu and Andrew Christlieb 3 Abstract In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially nonoscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear...
متن کامل