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    A numerical solution of the Boussinesq equations based on a Godunov-type FVM
    (American Society of Civil Engineers (ASCE), 2005) Ilic S.; Erduran K.; Kutija V.
    The paper summarizes a numerical solution based on a Godunov-type finite-volume method of the Boussinesq-type equations. A new hybrid solution incorporates the finite-volume method for the solution of the conservative part of the equations and the finite-difference method for the solution of the high order Boussinesq terms. The numerical model predictions are in close agreement with the theoretical predictions and those previously published for different numerical solutions. The model tests presented here showed that the model performance is primarily dependent on the linear dispersion approximation in the governing equations. Additionally, the model accuracy and computation efficiency is affected by numerical methods applied within the hybrid solution, in particular with slope limiters for the data construction in high-order finite-volume solution. This newly developed model accurately predicts wave propagation in deep water and over sloping beds.
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    Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations
    (2005) Erduran K.S.; Ilic S.; Kutija V.
    A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd.