  A fully discrete energy stability analysis is carried out for linear
advection-diffusion problems discretized by generalized upwind
summation-by-parts~(upwind gSBP) schemes in space and implicit-explicit
Runge-Kutta~(IMEX-RK) schemes in time. Hereby, advection terms are discretized
explicitly while diffusion terms are solved implicitly. In this context,
specific combinations of space and time discretizations enjoy enhanced
stability properties. In fact, if the first and second-derivative upwind gSBP
operators fulfill a compatibility condition, the allowable time step size is
independent of grid refinement, although the advective terms are discretized
explicitly. In one space dimension it is shown that upwind gSBP schemes
represent a general framework including standard discontinuous Galerkin~(DG)
schemes on a global level. While previous work for DG schemes has demonstrated
that the combination of upwind advection fluxes and the central-type first
Bassi-Rebay~(BR1) scheme for diffusion does not allow for grid-independent
stable time steps, the current work shows that central advection fluxes are
compatible with BR1 regarding enhanced stability of IMEX time stepping.
Furthermore, unlike previous discrete energy stability investigations for DG
schemes, the present analysis is based on the discrete energy provided by the
corresponding SBP norm matrix and yields time step restrictions independent of
the discretization order in space since no finite-element-type inverse
constants are involved. Numerical experiments are provided confirming these
theoretical findings.
