Improvement of the WENO Scheme Smoothness Estimator
نویسندگان
چکیده
This paper has analyzed the weights of the 5th order WENO (weighted essentially non-oscillatory) scheme suggested by Jiang and Shu and a modified smoothness estimator is suggested to improve the accuracy. Several numerical tests are presented to demonstrate the accuracy and robustness of the new scheme.
منابع مشابه
An 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 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 کاملcient Implementation of Weighted ENO Schemes 1
In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite diierence schemes of Liu, Osher and Chan 9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r +1) th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of...
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 کاملAn 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 کامل