五阶WENO格式求解一维Euler方程

Fifth Order WENO Scheme for Solving One-dimensional Euler Equations

应用加权本质无震荡(WENO)格式耦合低耗散E-CUSP格式,空间采用低耗散E-CUSP迎风格式,时间采用显式Runge-Kutta推进方法,分别对一维激波管问题和一维低密度流问题进行了数值模拟,发现WENO格式耦合低耗散E-CUSP算法在接触间断和激波处的捕捉效果有了显著地提高。结果表明,WENO格式精度高,稳定性能好,将WENO格式耦合低耗散E-CUSP算法应用到一维Euler方程的数值解中,对接触间断和激波的捕捉能力较强,尤其是对激波的捕捉能力,仅需要2～3个网格单元,为后续将其推广到二维问题上做了良好的铺垫。

The performance of coupled low dissipation E-CUSP scheme with high precision weighted essentially non-oscillatory WENO scheme is investigated by solving the one-dimensional shock tube problem and the one-dimensional low density flow problem.With the space adopts the low-dissipation E-CUSP upwind scheme and the time adopts the explicit Runge-Kutta propulsion method.It is found that WENO scheme coupled with low dissipation E-CUSP scheme in space.The capture effect of -CUSP algorithm in contact discontinuities and shock waves has been significantly improved.The results show that the WENO scheme has high accuracy and good stability.And WENO scheme coupled with low dissipation E-CUSP algorithm is applied to the numerical solution of one-dimensional Euler equation.It has strong ability to capture contact discontinuities and shock waves,especially for shock waves,only two or three grid elements are needed.It lays a good foundation for extending it to two-dimensional problems.