Development of A 2D Numerical Model for Pollutant Transport using FTCS Scheme and Numerical Filter

Authors

Tias Ravena Maitsa, Civil Engineering Master Program, Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Bandung 40135, IndonesiaFollow
Qalbi Hafiyyan, Civil Engineering Master Program, Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Bandung 40135, Indonesia
Mohammad Bagus Adityawan, Department of Water Resources Engineering and Management, Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Bandung 40135, Indonesia
Ikha Magdalena, Industrial and Financial Mathematics Research Group, Institut Teknologi Bandung, Bandung 40135, Indonesia
Arno Adi Kuntoro, Department of Water Resources Engineering and Management, Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Bandung 40135, Indonesia
Hadi Kardhana, Water Resources Engineering Research Group, Institut Teknologi Bandung, Bandung 40135, Indonesia

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.

Bahasa Abstract

Pengembangan Model Numerik 2D untuk Transpor Polutan dengan Skema FTCS dan Numerical Filter. Studi ini mengunakan metode beda hingga untuk mengembangkan suatu model numerik pada simulasi fenomena transpor polutan. Secara matematis, fenomena ini seringkali digambarkan dengan persamaan differensial adveksi-difusi yang merupakan gabungan dari persamaan kontinuitas dan hukum pertama Fick. Skema Forward Time Central Space (FTCS) adalah salah suatu metode eksplisit beda hingga dan digunakan dalam pemodelan pada studi ini karena kesederhanaannya dalam menyelesaikan suatu persamaan differensial. Namun, metode ini kurang stabil sehingga dapat menimbulkan osilasi pada model. Oleh karena itu, suatu numerical filter (Hansen) digunakan pada metode FTCS ini untuk meningkatkan stabilitas dari model. Model numerik yang telah dikembangkan diaplikasikan pada beberapa kasus transpor polutan 1D dan 2D. Hasil simulasi model dibandingkan dengan solusi analitik untuk memverifikasi model yang telah dikembangkan. Hasil tersebut menunjukkan bahwa model yang telah dikembangkan dapat mensimulasikan fenomena transpor polutan dengan baik. Selain itu, numerical filter juga dapat meningkatkan stabilitas model.

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Recommended Citation

Maitsa, Tias Ravena; Hafiyyan, Qalbi; Adityawan, Mohammad Bagus; Magdalena, Ikha; Kuntoro, Arno Adi; and Kardhana, Hadi (2021) "Development of A 2D Numerical Model for Pollutant Transport using FTCS Scheme and Numerical Filter," Makara Journal of Technology: Vol. 25: Iss. 3, Article 3.
DOI: 10.7454/mst.v25i3.3966
Available at: https://scholarhub.ui.ac.id/mjt/vol25/iss3/3