You can now run simulations using the fully nonlinear extended Boussinesq equations. The implementation follows the equation and numerical model presented in Kim et al., 2009, minus the horizontal rotational terms. The equations are the conservative form of the Wei et al. model, also presented in Shi et al, 2012. The numerical scheme is a hybrid finite-volume / finite-difference approach, with leading order terms solved in a similar way as the standard Celeris solver, but using a 4th-order MUSCL-TVD scheme and an HLLEM flux solver, with a 4th order predictor-corrector time stepping integration. The implementation is essentially the finite-volume version of COULWAVE - very similiar to FUNWAVE-TVD. Tests show accuracy similar to these models.
The fully nonlinear / high order model should be considered experimental, and is likely not as stable / robust as the standard Celeris solver, particularly when interacting with the simulation (changing depth on the fly, etc.). The fully nonlinear / high order model runs 20-40% slower than the standard Celeris solver.
Right now, the fully nonlinear / high order model can only be turned on for custom json configurations (no options to turn on in the GUI). To solve the fully nonlinear extended Boussinesq equations, set "NLSW_or_Bous" to "2' . While it is not necessary to solve the fully nonlinear model with a high-order numerical solver, this is recommended and provides numerical-physical consistency (the truncation error of the numerical scheme has a derivative order that is higher than any derivatives in the actual equations). To use the high-order solver, set "Accuracy_mode" to "1". Setting this value to "1" will have the numerical scheme use a 4th-order MUSCL-TVD scheme for the cell-face reconstruction of the primitive variables, as well as an HLLEM flux model. In summary: NLSW_or_Bous: 0 - NLSW equations [non-dispersive] NLSW_or_Bous: 1 - enhanced Boussinesq equations [weakly dispersive, weakly nonlinear]; standard Celeris model
NLSW_or_Bous: 2 - fully nonlinear extended Boussinesq equations [weakly dispersive+, fully nonlinear] Accuracy_mode: 0 - standard Celeris numerical scheme. 2nd-order cell-face reconstruction using the Generalised minmod limiter, and an HLL flux model. Accuracy_mode: 1 - high order numerical scheme. 4th-order reconstruction using a MUSCL-TVD scheme, and an HLLEM flux model, which maintains high-order accuracy in smooth regions. For field tests with random, directional waves, you are not likely to see large differences between these models unless the waves have significant energy in intermediate wave periods, where the better dispersion properties of the extended Boussinesq model are relevant. For large, narrow-banded waves, the fully nonlinear version may give markedly better predictions near the breakpoint and through the surf.