Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems
Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems
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DOI：
10.1016/j.jcp.2019.05.050
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
G. Fu;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
G. Fu;Chi-Wang Shu
针对一般非结构网格上的对称线性双曲系统，提出了一种能量守恒的间断伽辽金（DG）方法。当使用k次张量积多项式时，得到了半离散格式在一维和多维直角网格上k+ 1阶的最优先验误差估计。提出了一种高阶节能的Lax-Wendroff时间离散化方法。在一维和二维矩形和三角形网格上给出了大量的数值结果，以支持理论发现并评估新方法。对于本文所考虑的所有例子，发现一种特殊的方法（具有加倍的未知数）在三角网格上是最优收敛的。并将该方法与经典的（耗散的）上旋DG方法和带中心通量的（保守的）DG方法进行了比较。数值结果表明，该方法具有较好的长时间模拟性能。
We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order k+ 1 are obtained for the semi-discrete scheme in one dimension, and in multi-dimensions on Cartesian meshes when tensor-product polynomials of degree k are used. A high-order energy-conserving Lax-Wendroff time discretization is also presented. Extensive numerical results in one dimension, and two dimensions on both rectangular and triangular meshes are presented to support the theoretical findings and to assess the new methods. One particular method (with the doubling of unknowns) is found to be optimally convergent on triangular meshes for all the examples considered in this paper. The method is also compared with the classical (dissipative) upwinding DG method and (conservative) DG method with a central flux. It is numerically observed for the new method to have a superior performance for long time simulations.