Model Numerik 2-Dimensi Perambatan Gelombang pada Perairan Dalam Sampai Peraiaran Dangkal Menggunakan Persamaan Boussinesq

M. Cahyono, Alwafi Pujiraharjo

Abstract


Abstrak. Pada penelitian ini telah dikembangkan suatu model numerik 2-dimensi perambatan gelombang pada perairan relatif dalam sampai perairan dangkal. Model numerik didasarkan pada persamaan Boussinesq yang diturunkan oleh Nwogu [1993]. Persamaan Boussinesq diselesaikan dengan teknik pemisahan operator untuk menyederhakan penyelesaian masalah perambatan gelombang yang kompleks menjadi lebih sederhana dengan beberapa nilai awal yang meliputi masalah konveksi, propagasi, dan dispersi satu dimensi. Persamaan konveksi dan propagasi diselesaikan dengan skema beda hingga eksplisit MacCormack, sedangkan untuk suku-suku dispersi diselesaikan dengan skema beda hingga terpusat orde empat. Model diujikan untuk beberapa simulasi transformasi gelombang yaitu shoaling, refraksi, dan difraksi gelombang reguler pada beberapa kondisi batimetri hasil percobaan laboratorium oleh peneliti sebelumnya, seperti percobaan pengaruh perubahan kedalam terhadap refraksi-difraksi gelombang oleh Berkhoff dkk pada tahun 1982 [lihat Wei dan Kirby, 1998], percobaan refraksi-difraksi oleh Whalin pada tahun 1971 [lihat Wei dan Kirby, 1998] dan percobaan shoaling oleh Chawla [1995]. Perbandingan antara hasil-hasil simulasi model dengan data percobaan menunjukkan kemiripan. Hal ini membuktikan bahwa model yang dikembangkan mampu memprediksi transformasi gelombang akibat pengaruh pendangkalan dengan baik.

Abstract. Two-Dimensional model of wave propagation from relatively deep water to shallow water has been developed in this study. The model was based on the extended Boussinesq equations derived by Nwogu [1993]. The Equations were solved using a time splitting technique in which the two-dimensional Boussinesq equations were split into several one-dimensional initial value problems including convection, propagation and dispersion problems respectively. The convection and propagation problems were solved using Explicit MacCormack scheme while dispersion problems were solved using fourth order central scheme. The model has been used to simulate shoaling, refraction and diffraction of regular wave setup in laboratories by previous authors, including, effect of bathymetric variation to wave refraction-diffraction by Berkhoff et al in 1982 [Wei and Kirby, 1998], wave refraction-diffraction by Whalin in 1971 [Wei and Kirby, 1998] and shoaling experiment by Chawla [1995].  omparisons between the model predictions and data show good agreement. Thus, the model is capable of predicting wave transformation due to varying bathymetry.

Keywords


Persamaan Boussinesq; Dua-dimensi; Pemisahan operator; Shoaling; Refraksi; Difraksi; Gelombang reguler.

Full Text:

PDF

References


Abarbanel, S., Gottlieb, D., 1981, “Optimal Time Splitting for Two-and Three-Dimensional Navier-Stokes Equations with Mixed Derivatives”. Journal of Computational Physics. Vol. 41, 1 – 33.

Benque, J.P., Cunge, J.A., Feuillet, J., Hauguel, A., and Holly, Jr., F.M., 1982, “New Method for Tidal Current Computation”, Journal of Waterway, Port, Coastal, and Ocean Engineering Vol. 108, 397 – 417.

Cahyono, M., Falconer, R.A., 1997, “Optimal Time Splitting for Two- and Three-Dimensional Adjective-Diffusion Simulations Using Higher Order Finite Different Schemes”, In: Proc. Regional Seminar on Computational Method and Simulations in Engineering (CMSE’97), Institute Teknologi Bandung, pp.VII.C.5 1 - 10

Chawla. A., 1995, “Wave Transformation Over A Submerged Shoal”, A Thesis Submitted to

the Faculty of The University of Delaware in partial fulfillment of The Requirement for the Degree of Master of Civil Engineering.

Madsen, P.A., Murray, R., and Sorensen, O.R., 1991, “A New Form of The Boussinesq Equations with Improved Linear Dispersion Characteristics”. Coastal Engineering Vol. 15, 371 – 388.

Nwogu, O., 1993, “Alternative Form of Boussinesq Equations for Nearshore Wave Propagation”, Journal of Waterway, Port, Coastal, and Ocean Engineering Vol. 119 (6), 618 – 638.

Wei, G., Kirby, J.T., 1995, “Time-Dependent Numerical Code for Extended Boussinesq Equations", Journal of Waterway, Port, Coastal, and Ocean Engineering Vol. 121 (5), 251 – 261.

Wei, G., Kirby, J.T., 1998, “Simulation of Water Waves by Boussinesq Models", Research Report CACR-98-02. Center for Applied Coastal Research. Ocean Engineering Laboratory. University of Delaware.




DOI: http://dx.doi.org/10.5614%2Fjts.2005.12.4.4

Refbacks

  • There are currently no refbacks.


web
analytics

Lisensi Creative Commons

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License