Summation-by-Parts Finite-Difference Method for Linear Shallow Water Equations on Staggered Curvilinear Grids in Closed Domains

Abstract: This work focuses on developing high-order energy-stable schemes for wave-dominated problems in closed domains using staggered finite-difference summation-by-parts (SBP FD) operators. We extend the previously presented uniform staggered grid SBP FD approach to non-orthogonal curvilinear multi-block grids and derive new higher-order approximations. The combination of Simultaneous-Approximation-Terms (SAT) and projection method is proposed for the treatment of interface conditions on a staggered grid. This reduces approximation stiffness and mitigates stationary wave modes of pure SAT approach. Also, energy-neutral discrete Coriolis terms operators are presented. The proposed approach is tested using the linearized shallow water equations on a rotating sphere, a testbed relevant for ocean and atmospheric dynamics. Numerical experiments show significant improvements in capturing wave dynamics compared to collocated SBP FD methods.