TY - JOUR

T1 - Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

AU - Chesnokov, Alexander

AU - Nguyen, Trieu Hai

PY - 2019/7/15

Y1 - 2019/7/15

N2 - We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk et al. (2016). The use of this system for modelling the evolution of surface waves makes it possible to avoid the major numerical challenges in solving dispersive shallow water equations, which are connected with the resolution of an elliptic problem at each time instant and realization of non-reflecting conditions at the boundary of the calculation domain. It also allows one to reduce the computation time. The velocities of the characteristics of the obtained model are determined and the linear analysis is performed. Stationary solutions of the model are constructed and studied. Numerical solutions of the hyperbolic system are compared with solutions of the original dispersive model. It is shown that they almost coincide for large time intervals. The system obtained is applied to study non-stationary undular bores produced after interaction of a uniform flow with an immobile wall, non-hydrostatic shear flows over a local obstacle and the evolution of breaking solitary wave on a sloping beach.

AB - We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk et al. (2016). The use of this system for modelling the evolution of surface waves makes it possible to avoid the major numerical challenges in solving dispersive shallow water equations, which are connected with the resolution of an elliptic problem at each time instant and realization of non-reflecting conditions at the boundary of the calculation domain. It also allows one to reduce the computation time. The velocities of the characteristics of the obtained model are determined and the linear analysis is performed. Stationary solutions of the model are constructed and studied. Numerical solutions of the hyperbolic system are compared with solutions of the original dispersive model. It is shown that they almost coincide for large time intervals. The system obtained is applied to study non-stationary undular bores produced after interaction of a uniform flow with an immobile wall, non-hydrostatic shear flows over a local obstacle and the evolution of breaking solitary wave on a sloping beach.

KW - Dispersive shallow water equations

KW - Hyperbolic systems

KW - Shear flows

KW - ROLL-WAVES

KW - DERIVATION

KW - BREAKING

KW - BOUNDARY-CONDITIONS

KW - FAVRE-WAVES

KW - EQUATIONS

KW - LAYER

UR - http://www.scopus.com/inward/record.url?scp=85066104771&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2019.05.017

DO - 10.1016/j.compfluid.2019.05.017

M3 - Article

AN - SCOPUS:85066104771

VL - 189

SP - 13

EP - 23

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

ER -