A large time-step and well-balanced Lagrange-Projection type scheme for the shallow-water equations
For computational fluid dynamics practitioners, this method improves efficiency in simulating shallow-water flows by allowing larger time steps without sacrificing accuracy.
The paper extends implicit-explicit schemes to shallow-water equations, enabling large time steps unrestricted by sound velocity while maintaining accuracy and well-balanced properties. Numerical tests confirm stability and performance.
This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of compressibleflows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the well-known well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases.