An improved WENO scheme with a new smoothness indicator
نویسندگان
چکیده
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 WENO schemes called as WENO-M [8] and WENO-Z [2], but its advantage seems more salient in two dimensional problems. Some numerical experiments are presented to demonstrate the performance of the proposed scheme.
منابع مشابه
Improved Seventh-Order WENO Scheme
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 indic...
متن کاملMapped Weno Schemes Based on a New Smoothness Indicator for Hamilton-jacobi Equations
In this paper, we introduce an improved version of mapped weighted essentially nonoscillatory (WENO) schemes for solving Hamiton-Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et. al. [24]. The proposed scheme yields fifth-order accuracy in smooth regi...
متن کاملHigh order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
In ([10], JCP 227 No. 6, 2008, pp. 3101–3211), the authors have designed a new fifth order WENO finite-difference scheme by adding a higher order smoothness indicator which is obtained as a simple and inexpensive linear combination of the already existing low order smoothness indicators. Moreover, this new scheme, dubbed as WENO-Z, has a CPU cost which is equivalent to the one of the classical ...
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 کاملImprovement of weighted essentially non-oscillatory schemes near discontinuities
In this article, we analyze the fifth-order weighted essentially non-oscillatory(WENO-5) scheme and show that, at a transition point from smooth region to a discontinuity point or vice versa, the accuracy order of WENO-5 is decreased. A new method is proposed to overcome this drawback by introducing 4th-order fluxes combined with high order smoothness indicator. Numerical examples show that the...
متن کامل