适用于间断Galerkin方法的限制器研究

Investigation of a slope limiter for Runge-Kutta discontinuous Galerkin methods

开发了一种适用于高精度间断Galerkin方法的斜率(多项式系数)限制器。与现有的斜率限制器不同,该限制器实施过程不考虑网格单元类型(三角形或四边形),通过全微分方法构造新的多项式系数,因此,该限制器能够适用于各种类型网格———结构化网格、具有单一单元的非结构化网格和具有混合单元的非结构化网格。由于该限制器能够方便地应用于具有混合单元的非结构化网格,因此,本文使用的程序能够方便地求解具有复杂几何结构的流动问题。本文利用一些典型算例对其性能进行了验证,表明该限制器适用于不同类型的网格单元,能够在光滑解区保证高的精度,并能够在间断区抑制非物理振荡。

A new slope limiter was formulated for the discontinuous Galerkin methods in this paper. Unlike the previous slope limiters, this slope limiter reconstructed the new gradients for limiting by using the total differential method and took no account of the element types. Consequently, it can be adopted on structured grids, pure-element unstructured grids and mixed-element unstructured grids,leading to a ver- satile limiter to resolve more effectively complex geometry problems. The developed slope limiter was used in a discontinuous Galerkin method to compute a variety of flow problems. The numerical results show its capability to different types of elements, to preserve the accuracy in smooth regions as well as to prevent spurious oscillations near solution discontinuities.