Local Characteristic Decomposition Based Central-Upwind Scheme
Local Characteristic Decomposition Based Central-Upwind Scheme
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DOI：
10.1016/j.jcp.2022.111718
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Alina Chertock;Shaoshuai Chu;M. Herty;A. Kurganov;M. Lukáčová-Medvid’ová
中科院分区：
文献类型：
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作者：
Alina Chertock;Shaoshuai Chu;M. Herty;A. Kurganov;M. Lukáčová-Medvid’ová
我们提出了新的少扩散格式的保守的一维和二维双曲型非线性偏微分方程组（PDE）。为所研究的系统开发准确和鲁棒的数值方法的主要挑战来自复杂的波结构，例如冲击、稀疏和接触不连续性，即使在光滑的初始条件下也会出现。为了减少原中心迎风格式中的扩散，我们利用局部特征分解方法发展了一类新的中心迎风格式。我们应用开发的计划的一维和二维气体动力学欧拉方程，以说明各种例子上的性能。数值结果表明，新格式的性能优于原中心迎风格式。
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the studied systems come from the complicated wave structures, such as shocks, rarefactions and contact discontinuities, arising even for smooth initial conditions. In order to reduce the diffusion in the original central-upwind schemes, we use a local characteristic decomposition procedure to develop a new class of central-upwind schemes. We apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics to illustrate the performance on a variety of examples. The obtained numerical results clearly demonstrate that the proposed new schemes outperform the original central-upwind schemes.