Adaptive third order Adams-Bashforth time integration for extended Boussinesq equations

We develop the third-order adaptive Adams-Bashforth time integration 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. The newly added adaptive scheme significantly improves the robustness of the model while providing faster computational performance. 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.