کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4664924 | 1345314 | 2009 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Spectral/HP element method with hierarchical reconstruction for solving nonlinear hyperbolic conservation laws Spectral/HP element method with hierarchical reconstruction for solving nonlinear hyperbolic conservation laws](/preview/png/4664924.png)
The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM '07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential non-oscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.
Journal: Acta Mathematica Scientia - Volume 29, Issue 6, November 2009, Pages 1737-1748