Numerical Modeling of Mild Slope Equation with Finite Volume Method

Abstract When waves propagate from deep water to shallow water, they transform. Extended mild slope equation includes wave transformations such as refraction, diffraction, shoaling, reflection and dissipations due to bottom friction and wave breaking and harbour resonance. Extended mild slope equation can be applied to the rapidly varying topographies through higher order bottom effetcs. Nonlinear wave celerity and group velocity have been considered in the calculations. In this study, extended mild slope equation has been reduced to Helmholtz equation and solved with finite volume method. Numerical model has been tested on semicircular shoaling area and compared with the physical experiment measurements given in literarure. Numerical model has been applied to the Fethiye Bay in the Mediterranean Sea in Turkey. Key-words: Extended mild slope equation, finite volume method, wave refraction, diffraction, nonlinear wave celerity and group velocity