Adaptive Third Order Adams-Bashforth Time Stepping Scheme for 2D Extended Boussinesq Equations
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We develop the third-order adaptive Adams-Bashforth time stepping scheme and the second-order finite difference discretization equation for variable time steps. We incorporate these schemes in the Celeris Advent software to discretize and solve the extended Boussinesq equations. This software uses a hybrid finite volume - finite difference scheme and leverages GPU to solve the equations faster than real-time as well to concurrently visualize 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 without slowing it down.
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