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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Makara Journal of Technology
Magdalena, Ikha
Faculty Of Mathematics And Natural Sciences, Institut Teknologi Bandung, Indonesia
Chemical Engineering, Chemistry & Bioengineering Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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Development of A 2D Numerical Model for Pollutant Transport using FTCS Scheme and Numerical Filter Maitsa, Tias Ravena; Hafiyyan, Qalbi; Adityawan, Mohammad Bagus; Magdalena, Ikha; Kuntoro, Arno Adi; Kardhana, Hadi
Makara Journal of Technology Vol. 25, No. 3
Publisher : UI Scholars Hub

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Abstract

This study used the finite difference method to develop a numerical model for pollutant transport phenomenon simulation. Mathematically, the phenomenon is often described by the advection–diffusion differential equation, which is obtained from a combination of the continuity equation and Fick’s first law. The Forward Time Central Space (FTCS) scheme is one of the explicit finite difference methods and is used in this study to solve the model due to its simplicity in solving a differential equation. Yet, this method is currently unstable, which results in oscillations in the model. Thus, a numerical filter (Hansen) is added to the FTCS method to improve the stability of the model. The developed numerical model is applied to several 1D and 2D pollutant transport test cases. Simulation results are compared with those of existing analytical solutions to verify the developed model, and they show that the developed model can simulate the pollutant transport phenomenon well. Moreover, the numerical filter can increase the model stability.
THIN FILM FLOW ON AN INCLINED CHANNEL Leo Hari Wiryanto; Sudi Mungkasi; Ikha Magdalena
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp2151-2162

Abstract

A two-dimensional fluid is considered on an inclined channel. The depth of the fluid is small, so that it can be modeled as a single equation of the fluid depth, from the lubrication theory. The model is then solved numerically by an implicit finite difference method, to observe the surface wave propagation from the parameters such as the inclination of the channel and the ratio of the fluid thickness with respect to the wavelength. The effect of non-linearity of the model indicates that the wave propagates with changing the form, decreasing the amplitude, and tending to an almost shock wave. Those are simulated in this paper.
Co-Authors Adityawan, Mohammad Bagus Arno Adi Kuntoro Hadi Kardhana Hafiyyan, Qalbi Leo Hari Wiryanto Maitsa, Tias Ravena Sudi Mungkasi