eighted Taylor Series for Water Wave Modeling

This research builds upon Hutahaean (2024a), focusing on time series water wave modeling, with substantial portions of this article derived from that prior study. Modifications were made to the calculation algorithm; specifically, vertical water particle velocity is now computed using the continuity equation, and water surface elevation is determined through kinematic free surface boundary conditions. While this revised algorithm enables the model to simulate wave breaking, it results in an excessively high breaker height and struggles to accurately simulate wave conditions post-breaking, particularly at large wave heights. To address these challenges, the kinetic energy conservation equation was integrated into the model. This addition facilitated the creation of a water surface elevation equation through the superposition of kinematic free surface boundary conditions and the kinetic energy conservation equation. This integration yields an equation that maintains a balance between changes in potential energy and changes in kinetic energy, enhancing the model’s capability to simulate both the shoaling-breaking process and subsequent wave conditions in shallow waters more effectively.

Section: Fig (11) Sloping Sea Bedmentioning

confidence: 93%

Section: Fig (11) Sloping Sea Bedmentioning

confidence: 97%

Section: Weighted Taylor Seriesmentioning

confidence: 99%

Section: Weighted Taylor Seriesmentioning

confidence: 99%

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Alternative Algorithms for Time Series Water Wave Modeling

Hutahaean

2024

“…This relationship indicates that an increase in ε directly amplifies the impact of higher-order Taylor series terms on the analysis. Although the methodology for determining these coefficients is elaborated in Hutahaean (2023a), it is important to emphasize that the accuracy of the coefficients listed in Table 1 significantly exceeds those previously reported by Hutahaean (2023a), reflecting advancements in the precision of incorporating higher-order differential terms to enhance the model's predictive accuracy and reliability in hydrodynamic evaluations. 𝜀 is the optimization coefficient, where in this time series model the selection of the weighting coefficient is determined by the wave amplitude the greater the wave amplitude the greater the 𝜀, which is in the range of 0.015 < 𝜀 < 0.035.…”

Section: IImentioning

confidence: 95%

Applying Weighted Taylor Series on Time Series Water Wave Modeling

Hutahaean

2024

This study develops a time series model for water waves using a weighted Taylor series approach to analyze water wave dynamics. The model incorporates the continuity equation, Euler's momentum conservation equation, and the Kinematic Free Surface Boundary Condition, all formulated through the weighted Taylor series. By integrating the modified continuity equation across the water depth, utilizing depth-averaged velocity concepts, we derive the water surface elevation equation. Similarly, applying the Euler momentum conservation principle to the water surface yields an equation for the horizontal water particle velocity, which is subsequently converted into an expression for the horizontal depth-averaged velocity. The equations for water surface elevation and horizontal water particle velocity are solved using numerical methods. The application of the numerical model results in the generation of four distinct wave profiles: sinusoidal, Stokes, cnoidal, and solitary wave profiles, classified according to Wilson's (1963) criteria. The emergence of each wave profile type is influenced by the specified input wave height.

Method for Determining Weighting Coefficients in Weighted Taylor Series Applied to Water Wave Modeling

Hutahaean

2023

The Weighted Taylor series is an adaptation of the conventional Taylor series truncated to the first order, wherein high-order differential terms are replaced by introducing weighting coefficients to the initial terms. This study presents a novel approach for computing these weighting coefficients specifically designed for water wave modeling. Subsequently, the derived weighted Taylor series is employed to formulate both weighted continuity and the weighted Laplace equation. The weighted Laplace equation facilitates the formulation of the velocity potential equation, leading to the development of wave transformation equations encompassing important phenomena such as shoaling, breaking, and refraction-diffraction. Additionally, the formulation of the weighted Euler momentum conservation equation is introduced to determine the wave number in deep water. By scrutinizing the outcomes of dispersion equations, as well as analyzing shoaling-breaking and refraction-diffraction scenarios, optimal values for the weighting coefficients are identified..