ImEx Stability with Applications to the Dispersive Shallow Water Equations
Presenter
January 10, 2022
Abstract
The dispersive shallow water equations (DSWE) are fluid models, applicable to coastal regions that include additional physics (such as dispersion) to the well-known shallow water equations. The DSWEs present several challenges for efficient time-stepping including mixed space and time derivatives, nonlinearities and higher order spatial derivatives. We present semi-implicit high-order time stepping strategies that avoid a fully implicit treatment of the nonlinear terms and simplify the treatment of the mixed space-time derivatives. The approach is based on extensions of a recent unconditional stability theory, where due to the structure of the equations, zero stability plays the role of unconditional stability.