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We propose IMEX HDG-DG schemes for planar and spherical shallow watersystems. Of interest is subcritical flow, where the speed of the gravity waveis faster than that of nonlinear advection. In order to simulate these flowsefficiently, we split the governing system into a stiff part describing thegravity wave and a non-stiff part associated with nonlinear advection. Theformer is discretized implicitly with the HDG method while an explicitRunge-Kutta DG discretization is employed for the latter. The proposed IMEXHDG-DG framework: 1) facilitates high-order solutions both in time and space;  2) avoids overly small time-step sizes;  3) requires only one linear system solve per time stage;  4) relative to DG generates smaller and sparser linear systems whilepromoting further parallelism. Numerical results of various test casesdemonstrate that our methods are comparable to explicit Runge-Kutta DG schemesin terms of accuracy while allowing for much larger time step sizes.

IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin (HDG) and explicit discontinuous Galerkin (DG) approach for shallow water systems