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All Journal Jurnal Matematika Journal of the Indonesian Mathematical Society
Sulvianuri, Rani
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Mathematics

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Implementasi Numerik Berbagai Kondisi Batas pada Persamaan Air Dangkal Menggunakan Metode Elemen Hingga Terbaru Konformal dan Non-Konformal Swastika, Pt Veri; Sulvianuri, Rani; Gautama, I Putu Winada
Jurnal Matematika Vol 14 No 1 (2024)
Publisher : Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2024.v14.i01.p168

Abstract

In this paper, we extend the capability of a newly developed numerical scheme based on our preceding linear conformal and non-conformal finite element methods (FEM) to study 2D shallow water equations (SWE) with various boundaries. Unlike usual approach, we approximate the unknown in a staggered grid due to the use of linear alternating basis. Here, the free surface is approximated using a conformal while the velocity potential is approximated using a non-conformal linear basis. As a result, the varational problem must be reformulated. The resulting scheme is a ODE system which is easy to solve by any time integration method. Therefore, our method is staggered in space, explicit, flexible and simple to implement. The simulation results show that the flexibility of the scheme can be interpreted as the successful use of various boundary conditions. Keywords: 2D SWE, staggered finite element, non-conformal basis, influx boundary
Simulation of Tsunami Waves Generated by Landslide Movements on a Flat Bottom Sulvianuri, Rani; Setyowisnu, Glagah Eskacakra; Pudjaprasetya, Sri Redjeki
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1897

Abstract

Disasters like tsunamis are typically triggered by tectonic earthquakes, volcanic eruptions, or landslides. Tsunami waves can hit the coast with enormous energy, causing great damage. This study focuses on landslide-generated wave phenomena; the analytical formula of the linear dispersive model is adopted and used to simulate the development of free surface waves due to bottom landslides. Various types of landslide motion were simulated over a flat bottom depth and the resulting surface wave forms were examined and compared with the far-field leading wave type of solution. In addition, the effect of wave dispersion on the resulting wave pattern was investigated.
Co-Authors I PUTU WINADA GAUTAMA Setyowisnu, Glagah Eskacakra Sri Redjeki Pudjaprasetya, Sri Redjeki Swastika, Pt Veri