عنوان انگلیسی مقاله:
Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws
ترجمه فارسی عنوان مقاله:
نشانگر صافی ساده WENO-Z برای قوانین حفاظت از hyperbolic
Sciencedirect - Elsevier - Applied Numerical Mathematics, 157 (2020) 255–275: 10:1016/j:apnum:2020:06:006
SamalaRathana, NagaRajuGandeb, Ashlesha A.Bhiseb
The advantage of WENO-JS scheme (1996) over the WENO-LOC scheme (1994) is that the WENO-LOCnon-linear weights do not achieve the desired order of convergence in smooth monotone regions and at regions containing critical points. In this article, this drawback is overcome with the WENO-LOC smoothness indicators by constructing ‘WENO-Z type’ non-linear weights with a novel global smoothness indicator. This novel smoothness indicator measures the derivatives of the reconstructed flux in a global stencil. 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 non-linear weights are studied. Numerical tests for scalar, one and two-dimensional system of Euler equations are presented to show the effective performance of the proposed numerical scheme.
Keywords: Hyperbolic conservation laws | WENO scheme | Discontinuity | Smoothness indicators | Non-linear weights | Finite difference scheme