The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly d...The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland＇s hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit （ADI） method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50839001, 50979036)the National Science and Technology Major Special Project of China on Water Pollution Control and Management (Grant No. 2009ZX07528-006-01)
文摘The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland＇s hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit （ADI） method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.
