一种求解双曲守恒律方程的中心型WENO格式  

A CENTRAL WENO SCHEME FOR HYPERBOLIC CONSERVATION LAWS

作　　者：李辰 郭启龙[1,2] 孙东[1,2] 刘朋欣 Li Chen;Guo Qilong;Sun Dong;Lin Pengxin(State Key Laboratory of Aerodynamics,China Aerodynamnics Research and Development Center,Mianyang 621000,China;Computational Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]中国空气动力研究与发展中心,空气动力学国家重点实验室,绵阳621000 [2]中国空气动力研究与发展中心,计算空气动力研究所,绵阳621000

出　　处：《数值计算与计算机应用》2020年第3期246-258,共13页Journal on Numerical Methods and Computer Applications

基　　金：国家数值风洞工程,中国空气动力研究与发展中心前沿技术研究基金(PJD20180204);国家自然科学基金(11802324)资助.

摘　　要：本文发展了一种中心型加权本质无振荡(WENO)格式该格式通过在原始三阶WENO-JS格式的下风方向增加一个两点候选模板,并将文献[11]中的非线性自适应机制推广到r=2情况,格式记为WENO4-CU.经过近似色散关系分析可以看到,WENO4-CU格式的频谱特性较原始三阶WENO-JS格式具有明显的改进.通过六个典型算例的数值测试表明,WENO4-CU格式在对流动结构的分辨上较原始WENO3-JS、WENO3-M和WENO3-Z格式具有明显提高.A central weighted essentially non-oscillatory(WENO)scheme is presented in this paper.A two-point candidate sub-stencil is added downwind based on the third-order WENO-JS scheme,and the nonlinear adaption mechanism of reference[11]is extended to the version ofr=2.The scheme is named as WENO4-CU,the spectral properties of which are improved compared with the original third-order WENO-JS through approximate dispersion relation analysis.Numerical tests of six benchmarks demonstrate that the WENO4-CU scheme has better performance in contrast with WENO3-JS,WENO3-M and WENO3-Z schemes on resolving flow structures.

关 键 词：WENO 光滑度量因子 有限差分格式 双曲守恒律 

分 类 号：O241.82[理学—计算数学]