【摘要】 针对S aint-Venant方程组提出了一种具有二阶精度的非交错中心有限体积格式.相较于经典中心格式为维持静稳态解选择重构守恒变量和水位值,但在求解移动稳态问题时会产生巨大误差,格式通过重构守恒变量和能量值,以及一种新的源项离散方法能够精确维持移动稳态解并捕捉其小扰动.最后,通过一些经典数值算例验证了格式的收敛性,谐性以及稳健性.更多还原

【Abstract】 In this paper,we propose a second-order unstaggered central finite volume scheme for the Saint-Venant system.Classical central scheme can preserve still-water steady state solution by reconstructing conservative variables and the water level,but generates enormous numerical oscillation when considering moving-water steady state.We choose to reconstruct conservative variables and the energy,and design a new discretization of the source term to preserve moving-water equilibria and capture its small perturbations.In the end,several classical numerical experiments are performed to verify the proposed scheme which is convergent,well-balanced and robust.更多还原