Runge-Kutta discontinuous Galerkin methods with WENO limiter for the special relativistic hydrodynamics
Runge-Kutta discontinuous Galerkin methods with WENO limiter for the special relativistic hydrodynamics
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DOI：
10.1016/j.jcp.2013.02.018
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
Jian Zhao;Huazhong Tang
中科院分区：
文献类型：
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作者：
Jian Zhao;Huazhong Tang
本文针对一维和二维狭义相对论流体力学，K=1,2,3，开发了带有 WENO 限制器的基于 PK 的龙格-库塔不连续伽辽金 (RKDG) 方法，这是该工作的扩展 [J.X.邱，C.-W。 Shu，使用 WENO 限制器的 Runge-Kutta 不连续 Galerkin 方法，SIAM J. Sci。计算。 26（2005）907-929]。 RKDG方法的WENO限制器通过以下两个步骤自适应地实现：首先使用TVB修改的minmod函数识别“问题”小区，然后基于相邻小区中RKDG解的小区平均值以及“问题”小区的原始小区平均值，使用WENO技术局部重建“问题”小区内的新多项式解以替换RKDG解。使用开发的 RKDG 方法和 WENO 限制器计算一维和二维的几个测试问题。计算表明，我们的方法在保持特殊相对论流体力学中模拟流动的精度方面是稳定、准确和稳健的。
This paper develops the PK-based Runge–Kutta discontinuous Galerkin (RKDG) methods with WENO limiter for the one- and two-dimensional special relativistic hydrodynamics, K=1,2,3, which is an extension of the work [J.X. Qiu, C.-W. Shu, Runge–Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput. 26 (2005) 907–929]. The WENO limiter for the RKDG method is adaptively implemented via two following steps: the “troubled” cells are first identified by using a TVB modified minmod function, and then a new polynomial solution inside the “troubled” cells is locally reconstructed to replace the RKDG solution by using the WENO technique based on the cell average values of the RKDG solution in the neighboring cells as well as the original cell averages of the “troubled” cells. Several test problems in one and two dimensions are computed using the developed RKDG methods with WENO limiter. The computations demonstrate that our methods are stable, accurate, and robust in maintaining accuracy for simulating flows in the special relativistic hydrodynamics.