A Continuity Equation For Time Series Water Wave Modeling Formulated Using Weighted Total Acceleration

Abstract

Continuity equation for wave modeling is still being developed. There are quite a lot of versions of this equation. This research formulates continuity equation in a simple form to simplify its numerical and analytical solution. The formulation of the continuity equation is done by performing mass conservation law in a water column with free surface and by performing weighted total acceleration. Then, the continuity equation is performed along with the surface momentum equation and completed numerically to modeling one-dimensional wave dynamism. The equation is capable of modeling shoalingand breaking.

Alternative Algorithms for Time Series Water Wave Modeling

“…The wave height is reduced from 𝐻 = 2.60 𝑚 to 2.50 𝑚, that is assumed due to deflection in the form of small wave. In Fig (10), the model execution results at water depth ℎ = 8.0 𝑚 are presented, three wave crests are formed, the largest of which is the main wave. In this case, the main wave can be classified as a solitary wave with wave height 𝐻 = 2.20 𝑚, considering that the entire wave body is above the still water level.…”

“…Fig (9). Cnoidal wave profile, 𝐴 = 1.30 𝑚, ℎ = 20.0 𝑚 Fig (10). Solitary wave profile, 𝐴 = 1.30 𝑚, ℎ = 8.0 𝑚…”

eighted Taylor Series for Water Wave Modeling

“…Equation ( 6) is hereinafter referred to as the optimization equation. In (6), the variable to be calculated is . While is a very small number which will determine the level of accuracy.…”