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MacCormack method for solving one-dimensional bed-load sediment transport model

Metode MacCormack untuk menyelesaikan model transpor sedimen permukaan dasar satu dimensi

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 2 (2023) · pp. 412–422

DOI
10.20956/j.v19i2.24182
ISSN
2614-8811, 1858-1382
Published
2023-01-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

In this work, we investigate the numerical solution of one-dimensional bed-load sediment transport model using two steps finite difference method which so-called MacCormack method. Bed-load sediment transport model is composed by the shallow water equation and Exner equation. The Meyer-Peter and Muller (MPM) formula and Wu formula will be used to determine the Grass factor of the bed-load sediment transport. These governing equations will be discretized into predictor and corrector steps of the MacCormack method. The numerical results of the MacCormack method will be validated with an analytical solution of the bed-load sediment transport model. In addition, the MacCormack solution will also be compared with experimental solutions and another numerical method solutions that have existed previously. The numerical results based on MacCormack method give excellent results in which the numerical and the analytical results are hardly differentiated with RMSE of around 00042 or 4,2.

Bahasa Indonesia

Penelitian ini menyelidiki solusi numerik model transpor sedimen permukaan dasar menggunakan metode beda hingga dua step yang disebut metode MacCormack. Model transpor sedimen permukaan dasar dibangun atas persamaan air dangkal dan persamaan Exner. Formula Meyer-Peter dan Muller (MPM) dan formula wu akan digunakan untuk menentukan faktor Grass dari transpor sedimen permukaan dasar. Persamaan pembangun ini didiskritisasi kedalam step prediktor dan korektor dari metode MacCormack. Hasil numerik metode MacCormack akan divalidasi dengan sebuah solusi analitik dari model transpor sedimen permukaan dasar. Selain itu, solusi metode MacCormack juga akan dibandingkan dengan solusi-solusi eksperimen dan solusi-solusi metode numerik yang telah ada sebelumnya. Hasil numerik berdasarkan metode MacCormack memberikan hasil yang sangat baik dimana hasil numerik dan hasil analitik hampir tidak dapat dibedakan.

Keywords

Collaboration network of the authors

20 authors · 31 co-authorship links · 2 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • State University of Makassar
  • Universitas Muhammadiyah Malang
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Syamsuddin ToahaAffiliation unknown3
Amrul FaruqUniversitas Muhammadiyah Malang1
Merinda LestandyUniversitas Muhammadiyah Malang1
Oschar SumardinState University of Makassar1
Dewi Siti OktaviantiAffiliation unknown1
Alfonsa Reni OktaviaAffiliation unknown1
Rani Rahmasari TanuwijayaAffiliation unknown1
Yori YolandaAffiliation unknown1
Tati SuryatiAffiliation unknown1
Ria SimanungkalitAffiliation unknown1
Jusmawati MassalesseAffiliation unknown1
Jeffry KusumaAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Andi Galsan MahieAffiliation unknown1
Rezki Setiawan BachrunAffiliation unknown1
Aidawayati RangkutiAffiliation unknown1
Astri AksanAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">MacCormack method for solving one-dimensional bed-load sediment transport model</dc:title>
	<dc:title xml:lang="id">Metode MacCormack untuk menyelesaikan model transpor sedimen permukaan dasar satu dimensi</dc:title>
	<dc:creator xml:lang="en">Said, Irfan</dc:creator>
	<dc:creator xml:lang="en">Ribal, Agustinus </dc:creator>
	<dc:creator xml:lang="en">Khaeruddin, Khaeruddin</dc:creator>
	<dc:subject xml:lang="en">Bed-load sediment transport model</dc:subject>
	<dc:subject xml:lang="en">Shallow water equation</dc:subject>
	<dc:subject xml:lang="en">Exner equation</dc:subject>
	<dc:subject xml:lang="en">MacCormack Method</dc:subject>
	<dc:subject xml:lang="id">Model transpor sedimen permukaan dasar</dc:subject>
	<dc:subject xml:lang="id">Persamaan air dangkal</dc:subject>
	<dc:subject xml:lang="id">Persamaan Exner</dc:subject>
	<dc:subject xml:lang="id">Metode MacCormack</dc:subject>
	<dc:description xml:lang="en">In this work, we investigate the numerical solution of one-dimensional bed-load sediment transport model using two steps finite difference method which so-called MacCormack method. Bed-load sediment transport model is composed by the shallow water equation and Exner equation. The Meyer-Peter and Muller (MPM) formula and Wu formula will be used to determine the Grass factor of the bed-load sediment transport. These governing equations will be discretized into predictor and corrector steps of the MacCormack method. The numerical results of the MacCormack method will be validated with an analytical solution of the bed-load sediment transport model. In addition, the MacCormack solution will also be compared with experimental solutions and another numerical method solutions that have existed previously. The numerical results based on MacCormack method give excellent results in which the numerical and the analytical results are hardly differentiated with RMSE of around 00042  or 4,2 .</dc:description>
	<dc:description xml:lang="id">Penelitian ini menyelidiki solusi numerik model transpor sedimen permukaan dasar menggunakan metode beda hingga dua step yang disebut metode MacCormack. Model transpor sedimen permukaan dasar dibangun atas persamaan air dangkal dan persamaan Exner. Formula Meyer-Peter dan Muller (MPM) dan formula wu akan digunakan untuk menentukan faktor Grass dari transpor sedimen permukaan dasar. Persamaan pembangun ini didiskritisasi kedalam step prediktor dan korektor dari metode MacCormack. Hasil numerik metode MacCormack akan divalidasi dengan sebuah solusi analitik dari model transpor sedimen permukaan dasar. Selain itu, solusi metode MacCormack juga akan dibandingkan dengan solusi-solusi eksperimen dan solusi-solusi metode numerik yang telah ada sebelumnya. Hasil numerik berdasarkan metode MacCormack memberikan hasil yang sangat baik dimana hasil numerik dan hasil analitik hampir tidak dapat dibedakan.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-01-05</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/24182</dc:identifier>
	<dc:identifier>10.20956/j.v19i2.24182</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 2 (2023): JANUARY 2023; 412-422</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/24182/9163</dc:relation>
	<dc:relation>10.20956/j.v19i2.24182.g9163</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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