  We develop the third-order adaptive Adams-Bashforth time stepping and the
second-order finite difference equation for variable time steps. We incorporate
these schemes in the Celeris Advent software to discretize and solve the 2D
extended Boussinesq equations. This software uses a hybrid finite volume -
finite difference scheme and leverages the GPU to solve the equations faster
than real-time while concurrently visualizing them. We simulate several
benchmarks using the adaptive time stepping scheme of Celeris Advent and
demonstrate the capability of the software in modeling wave-breaking, wave
runup, irregular waves, and rip currents. The adaptive scheme significantly
improves the robustness of the model while providing faster computational
performance.
