Nested Schur-Complement Solver for a Low-Mach Number Model: Application to a Cyclone-Cyclone Interaction

Abstract

Forecasting the dynamical evolution of interacting tropical cyclones poses a computationally challenging problem. An attractive approach for modeling and simulating such type of dynamics is given by Low-mach models. A formulation of a Low-mach model is presented along with the description of a benchmark scenario of two interacting tropical cyclones. For the discrete nonlinear equations of this model, an improved variant of the nested Schur-complement preconditioner is proposed. A detailed discussion of the numerical results is conducted with a special emphasis on computational costs and scalability. It will be demonstrated that the new preconditioner clearly outperforms a prior version of this kind of preconditioner with respect to computing time by a factor of two, but at the cost of a slightly reduced scalability.