A coupled boundary element-finite difference solution of the elliptic modified mild slope equation.

*(English)*Zbl 1259.76031Summary: The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain with variable depth is solved by a flexible order of accuracy FDM in boundary-fitted curvilinear coordinates. The two solutions are matched along the common boundary of two methods (the BEM boundary) to ensure continuity of value and normal flux. Convergence of the individual methods is shown and the combined solution is tested against several test cases. Results for refraction and diffraction of waves from submerged bottom mounted obstacles compare well with experimental measurements and other computed results from the literature.

##### MSC:

76M15 | Boundary element methods applied to problems in fluid mechanics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

##### Keywords:

modified mild slope equation; wave diffraction; wave refraction; coupled boundary element-finite difference method; wave amplification##### Software:

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\textit{R. Naserizadeh} et al., Eng. Anal. Bound. Elem. 35, No. 1, 25--33 (2011; Zbl 1259.76031)

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