A well-balanced scheme for the shallow-water equations with topography

详细信息    查看全文

• 作者：Victor Michel-Dansac^a ; ^{victor.michel-dansac@univ-nantes.fr" class="auth_mail" title="E-mail the corresponding author} ; Christophe Berthon^a ; ^{christophe.berthon@univ-nantes.fr" class="auth_mail" title="E-mail the corresponding author} ; Sté ; phane Clain^b ; ^{clain@math.uminho.pt" class="auth_mail" title="E-mail the corresponding author} ; Franç ; oise Foucher^a ; ^c ; ^{francoise.foucher@ec-nantes.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Shallow-water equations ; Godunov-type schemes ; Well-balanced schemes ; Moving steady states
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：72
• 期：3
• 页码：568-593
• 全文大小：875 K

文摘

A non-negativity preserving and well-balanced scheme that exactly preserves all the smooth steady states of the shallow water system, including the moving ones, is proposed. In addition, the scheme must deal with vanishing water heights and transitions between wet and dry areas. A Godunov-type method is derived by using a relevant average of the source terms within the scheme, in order to enforce the required well-balance property. A second-order well-balanced MUSCL extension is also designed. Numerical experiments are carried out to check the properties of the scheme and assess the ability to exactly preserve all the steady states.