A central compact hybrid-variable method with spectral-like resolution: One-dimensional case
A central compact hybrid-variable method with spectral-like resolution: One-dimensional case
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DOI：
10.1016/j.cam.2022.114894
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
M. K. Hasan;Xianyi Zeng
中科院分区：
文献类型：
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作者：
M. K. Hasan;Xianyi Zeng
我们提出了一种具有谱精度的中心紧致混合变量方法(CHVM)来求解具有中等或较少间断的一阶双曲型问题。它结合了紧致差分策略和最近提出的混合变量离散化技术，在给定的网格单元模板上实现了更高的精度。首先对一维线性平流方程构造了CHVM，并进行了精度和稳定性分析，然后将其推广到一维非线性问题，如Burgers型方程和Euler方程。构造了一种新型的Gauss-Seidel型低通高阶滤波器，用于抑制不连续点附近的寄生振荡。通过广泛的基准测试评估了所提出方法的性能。
We present a central compact hybrid-variable method (CHVM) with spectral-like accuracy for first-order hyperbolic problems with moderate or less discontinuities. It incorporates the compact difference strategy and a recently proposed hybrid-variable discretization technique to achieve even higher accuracy on a given stencil of grid cells. The CHVM is first constructed for the one-dimensional (1D) model linear advection equations, in which case the accuracy and stability analysis are conducted; then it is extended to 1D nonlinear problems such as the Burgers’ equation and the Euler equations. A novel Gauss–Seidel type low-pass high-order filter is constructed to suppress spurious oscillations near discontinuities. The performance of the proposed method is assessed by extensive benchmark tests.