Abstract
Improved Weighted Essentially Non-oscillatory Scheme is a high order finite volume method. The mixed stencils can be obtained by a combination of r + 1 order and r order stencils. We improve the weights by the mapping method. The restriction that conventional ENO or WENO schemes only use r order stencils, is removed. Higher resolution can be achieved by introducing the r + 1 order stencils. This method is verified by three cases, i.e. the interaction of a moving shock with a density wave problem, the interacting blast wave problem and the double mach reflection problem. The numerical results show that the Improved Weighted Essential Non-oscillatory method is a stable, accurate high-resolution finite volume scheme.
Highlights
The ENO idea proposed in [1] seems to be the first successful attempt to obtain a self-similar, uniformly high order accurate, yet essentially non-oscillatory interpolation for piecewise smooth functions
We present the improved weighted essentially non-oscillatory (WENO) schemes by introducing a large mixed stencil, which is constructed by combining rth-order stencil and (r + 1)th-order stencil
In [4], optimum weights Ckr is introduced in the definition of ωk to make the WENO schemes achieve (2r − 1)th order accuracy in smooth domain
Summary
The ENO idea proposed in [1] seems to be the first successful attempt to obtain a self-similar, uniformly high order accurate, yet essentially non-oscillatory interpolation for piecewise smooth functions. The application of WENO schemes was expanded greatly, Johnsen and Colonius applied WENO schemes in compressible multicomponent flow problems [7], Caleffi, Valiani and Bernin [8] treated with fourth-order balanced source term in central WENO schemes for shallow water equations. These schemes only used rth-order stencils ignore larger than rth-order stencils without reference to ENO or WENO. It is possible to construct new WENO schemes by introducing larger than rth-order stencils. The numerical results show improved WENO schemes are the high resolution difference methods
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