Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Hybrid Finite-Volume Finite-Difference Scheme for the Solution of Boussinesq Equations.
AU - Erduran, K. S.
AU - Ilic, S.
AU - Kutija, V.
PY - 2005/12/20
Y1 - 2005/12/20
N2 - 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.
AB - 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.
KW - Keywords hybrid scheme � finite-volume scheme � Boussinesq model � fourth-order accuracy � deep-water wave propagation � deep to shallow water wave propagation
U2 - 10.1002/fld.1021
DO - 10.1002/fld.1021
M3 - Journal article
VL - 49
SP - 1213
EP - 1232
JO - International Journal for Numerical Methods in Fluids
JF - International Journal for Numerical Methods in Fluids
SN - 1097-0363
IS - 11
ER -