Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws
نویسندگان
چکیده
We describe briefly how a third-orderWeighted Essentially Nonoscillatory (WENO) scheme is derived by coupling aWENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative propertieswhenused to approximate the 1D linear advection equation anduse a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lower L 1 errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.
منابع مشابه
The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کاملCompact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws
The simulation of turbulent compressible flows requires an algorithm with high accuracy and spectral resolution to capture different length scales, as well as nonoscillatory behavior across discontinuities like shock waves. Compact schemes have the desired resolution properties and thus, coupled with a nonoscillatory limiter, are ideal candidates for the numerical solution of such flows. A clas...
متن کاملHigh Resolution Schemes for Hyperbolic Conservation Laws
A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux function. The so-derived second order accurate schemes achieve high resolution while preserving the robust...
متن کاملMaximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations
To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091–3120] to convection diffusion equations, we propose a nonconventional high order finite volume weighted essentially nonoscillatory (WENO) scheme which can be proved maximum-principle-satisfying. Two-dimensional extensions are straightforwa...
متن کاملENO and WENO Schemes
The weighted essentially nonoscillatory (WENO) schemes, based on the successful essentially nonoscillatory (ENO) schemes with additional advantages, are a popular class of high-order accurate numerical methods for hyperbolic partial differential equations (PDEs) and other convection-dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high-order form...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Mathematics
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013