Finite volume solution of boussinesq-type equations on an unstructured grid

A new numerical method is developed to solve a set of two-dimensional Boussinesq water wave evolution equations over an unstructured grid. The governing mass and momentum conservation equations are discretized over an irregular triangular grid, with a staggered placement of the variables. The free surface elevation is defined at the centroid of the triangles, while the normal component of the velocity is defined at the mid-point of the triangle edges. The mass conservation equation is then integrated over a control volume defined over each triangle while the momentum equations are integrated over a control volume formed from two adjacent triangles. A modified Crank-Nicolson scheme is used to integrate the equations in time. Two numerical experiments are used to evaluate the conservation properties and accuracy of the numerical method: solitary wave propagation in a curved channel, and interaction of solitary waves with a vertical circular cylinder.

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