High-Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Flows Along Channels with Irregular Geometry
摘要
In this paper, we present high-order well-balanced weighted compact nonlinear schemes (WCNSs) to solve shallow water equations in open channels with irregular geometry and non-flat bottom topography. To achieve numerical balance, we reformulate the governing equations into a pre-balanced equivalent form. In this form, the conserved variables remain time-independent in the steady-state solution, ensuring that the numerical scheme does not destroy the balance when reconstructing the conserved variables. Several advantages of the proposed schemes based on the development of governing equations in pre-balanced form. First, the reconstruction of the width and bottom topography variables is not required due to the pre-balanced operation. Second, the proposed schemes are high-order accuracy while maintaining the steady-state property, which we have theoretically proven. Several benchmark numerical examples demonstrate the effectiveness and superiority of the proposed schemes.