WENO‐Z schemeSummary This paper presents a new WENO‐Z scheme (WENO‐MZ) that incorporates a mapping function to enhance the weights of the less smooth sub‐stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub‐stencil to the smooth ...
10.6052/0459-1879-19-249AN IMPROVED FIFTH-ORDER WENO-Z+ SCHEME 1}Luo Xin W u Songping 2)(School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China)Abstract The performance improvement of the W E N O - Z + scheme depends on the role of the additional term ...
reliability of the above conclusion.The research in the present paper gives an improved method for third-order WENO-Z scheme:global smoothness indicators should be reasonably constructed to make scheme satisfy the requirement of design precision at non-critical points in the smoot...
WENO-Z schemecomputational techniquesIn this paper, a new WENO procedure is proposed to approximate the viscosity solution of the Hamilton鈥揓acobi (HJ) equations. In the one-dimensional (1D) case, an optimum polynomial on a six-point stencil is obtained. This optimum polynomial is fifth-order...
As a result, the proposed numerical scheme could decrease the dissipation near the discontinuous regions. The theoretical and numerical experiments to achieve the required order of convergence in smooth monotone regions, at critical points, and the essentially non-oscillatory (ENO) property of proposed...
The new scheme WENO-Z+ was shown to achieve even better results than WENO-Z, while keeping the same numerical robustness. In this study, the third- and seventh-order versions of the WENO-Z+ scheme are presented and discussed. The preliminary numerical results make evident that the approach ...
In this paper we recover a latent advantage of WENO-Z schemes. Taking the fifth-order WENO-Z scheme for instance, we realize that the scheme can be regarded as a nonlinear combination of a five-cells stencil and three three-cells stencils. The five-cells stencil is allotted a global ...
Although better resolution is achieved, it is shown in this article that, the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation. In order to fix the problem of WENO-Z, a symmetry-preserving mapping method is proposed in this ...
Based on the high-order global smoothness factor, a low-dissipation and high-resolution 3rd-order WENO difference scheme was obtained under the WENO-Z scheme framework. A parameter was introduced in the nonlinear weight, the parameter range was determined by convergence analysis, and the optimal ...
DEGENERATE parabolic equationsORTHOGONAL polynomialsThis paper provides a fourth-order scheme for approximating solutions of non-linear degenerate parabolic equations that their solutions may contain discontinuity. In the reconstruction step, a fourth-order weighted essentially non-oscillat...