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The momentum conservative scheme for simulating nonlinear wave evolution and run-up in U-shaped bays

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Abstract

This paper investigates a previously developed numerical algorithm; the scheme solves Saint-Venant type equations as a quasi-1-dimensional model for wave dynamics in U-bays. The first validation uses the N-wave initial surface in a parabolic bay; numerical surface and horizontal velocity on the shoreline agree well with analytical results. Furthermore, simulation of N-wave shoaling phenomenon in a parabolic bay agree well with the analytical run-up and run-down heights. In the wind set-up and set-down simulations, numerical results show good agreement with analytical prediction in terms of surface elevation and velocity at the shoreline. Next, we discuss general U-bays with two types of influx: solitary and monochromatic waves; good agreement with analytical formula is obtained for U-bays with various m. All of the preceding observations indicates the robustness of our momentum conserving staggered-grid (MCS) scheme to describe wave dynamics in U-bays.

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Acknowledgements

Financial support from Institut Teknologi Bandung and Indonesian Research Grant contract number 5S/IT1.C02/TA.00/2022 are greatly acknowledged.

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  1. Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia

    Sri Redjeki Pudjaprasetya & Rani Sulvianuri

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  1. Sri Redjeki Pudjaprasetya
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  2. Rani Sulvianuri
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Correspondence to Sri Redjeki Pudjaprasetya.

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Pudjaprasetya, S.R., Sulvianuri, R. The momentum conservative scheme for simulating nonlinear wave evolution and run-up in U-shaped bays. Japan J. Indust. Appl. Math. 40, 737–754 (2023). https://doi.org/10.1007/s13160-022-00549-4

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  • DOI: https://doi.org/10.1007/s13160-022-00549-4

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