论文标题
基于本地特征分解的中央风方案
Local Characteristic Decomposition Based Central-Upwind Scheme
论文作者
论文摘要
我们提出了针对非线性偏微分方程（PDES）的保守的一维双曲系统的新型扩散方案。研究系统的准确数值方法开发的主要挑战来自复杂的波结构，例如冲击，稀有因素和接触不连续性，即使是为了平稳的初始条件。为了减少原始中心风向方案中的扩散，我们使用局部特征分解程序来开发新的中央风向方案。我们将开发的方案应用于气体动力学的一维欧拉方程，以说明各种示例的性能。获得的数值结果清楚地表明，所提出的新方案的表现优于原始中心风项方案。
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.
