刘友琼, 刘庆升, 荣宪举, 黄封林. 一类求解浅水波方程的基本无振荡熵稳定格式[J]. 信阳师范学院学报(自然科学版), 2019, 32(3): 345-351. DOI: 10.3969/j.issn.1003-0972.2019.03.001
引用本文: 刘友琼, 刘庆升, 荣宪举, 黄封林. 一类求解浅水波方程的基本无振荡熵稳定格式[J]. 信阳师范学院学报(自然科学版), 2019, 32(3): 345-351. DOI: 10.3969/j.issn.1003-0972.2019.03.001
LIU Youqiong, LIU Qingsheng, RONG Xianju, HUANG Fenglin. Non-oscillatory Entropy Stable Scheme for Shallow Water Equations[J]. Journal of Xinyang Normal University (Natural Science Edition), 2019, 32(3): 345-351. DOI: 10.3969/j.issn.1003-0972.2019.03.001
Citation: LIU Youqiong, LIU Qingsheng, RONG Xianju, HUANG Fenglin. Non-oscillatory Entropy Stable Scheme for Shallow Water Equations[J]. Journal of Xinyang Normal University (Natural Science Edition), 2019, 32(3): 345-351. DOI: 10.3969/j.issn.1003-0972.2019.03.001

一类求解浅水波方程的基本无振荡熵稳定格式

Non-oscillatory Entropy Stable Scheme for Shallow Water Equations

  • 摘要: 针对浅水波方程,提出了一类低耗散基本无振荡熵稳定格式.在Roe型熵稳定通量中添加熵守恒格式的熵数值黏性绝对值的量来抵消解在跨过激波时所产生的熵增,从而抑制伪振荡;并且,利用通量限制器函数构造出相应的高分辨率熵稳定格式.利用新格式模拟一维和二维经典问题,数值结果表明,该格式具有低耗散、高分辨率、基本无振荡性等特点,是求解浅水波方程较为理想的方法.

     

    Abstract: A low dissipative non-oscillatory entropy stable scheme is presented for shallow water equations. The scheme is given to construct entropy stable flux by addition of the entropy viscosity term of entropy conservative flux into Roe's entropy stable flux, to controlling entropy production at discontinuities, which result have enough entropy dissipative to remove oscillations near discontinuity. Further, high resolution entropy stable flux is constructed for the flux limiter functions. These new fluxes is tested on one dimensional and two dimensional problems, numerical examples demonstrate that these schemes are low dissipative,high resolution and non-oscillatory.

     

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