Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows

Myong Chol Ri; Il Jang

doi:doi:10.11648/j.ajmie.20251005.12

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Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows

Myong Chol Ri^*

, Il Jang

Published in American Journal of Mechanical and Industrial Engineering (Volume 10, Issue 5)

Received: 12 August 2025 Accepted: 9 September 2025 Published: 26 November 2025

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Abstract

Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.

Published in	American Journal of Mechanical and Industrial Engineering (Volume 10, Issue 5)
DOI	10.11648/j.ajmie.20251005.12
Page(s)	96-100
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Shallow Water, Godunov Finite Volume Method, Local Time Stepping

References

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[2]	Sara Minisini and Elena Zhebel, “Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media”, GEOPHYSICS, VOL. 78, NO. 3.
[3]	Corey J. Trahan and Clint Dawson, “Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations”, Comput. Methods Appl. Mech. Engrg. 217-220 (2012) 139-152. https://doi.org/10.1016/j.cma.2012.01.002
[4]	Julien Diaz and Marcus J. Grote, “Multi-level explicit local time-stepping methods for second-order wave equations”, Comput. Methods Appl. Mech. Engrg. 291 (2015) 240-265. https://doi.org/10.1016/j.cma.2015.03.02
[5]	Ben R. Hodges., “A new approach to the local time stepping problem for scalar transport”, Ocean Modelling 77 (2014) 1-19. https://doi.org/10.1016/j.ocemod.2014.02.007
[6]	Farzam Safarzadeh Maleki and Abdul A. Khan, “A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework”, Applied Mathematical Modelling 40 (2016) 70-84. https://doi.org/10.1016/j.apm.2015.04.038
[7]	MARCUS J. GROTE and MICHAELA MEHLIN, “CONVERGENCE ANALYSIS OF ENERGY CONSERVING EXPLICIT LOCAL TIME-STEPPING METHODS FOR THE WAVE EQUATION”, Industrial and Applied Mathematics, Vol. 56, No. 2, pp. 994-1021. https://doi.org/10.1137/17M1121925
[8]	G. Jeanmasson and I. Mary, “On some explicit local time stepping finite volume schemes for CFD”, Journal of Computational Physics, 2019. https://doi.org/10.1016/j.jcp.2019.07.017
[9]	J. Rafael Cavalcanti and Michael Dumbser, “A Conservative Finite Volume Scheme with Time-Accurate Local Time Stepping for Scalar Transport on Unstructured Grids”, Advances in Water Resources, 2015. https://doi.org/10.1016/j.advwatres.2015.10.002
[10]	Walter Boscheri and Michael Dumbser, “High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes”, Journal of Computational Physics 291 (2015) 120-150. https://doi.org/10.1016/j.jcp.2015.02.052
[11]	Jeremy R. Lilly and Giacomo Capodaglio, “Storm Surge Modeling as an Application of Local Time-stepping in MPAS-Ocean”, Journal of Advances in Modeling Earth Systems (2022). https://doi.org/10.5281/zenodo.6908349
[12]	Shenghan Hu and Mengyao Zhang, “Numerical Solutions of the Nonlinear Dispersive Shallow Water Wave Equations Based on the Space-Time Coupled Generalized Finite Difference Scheme”, Applied sciences (2023). https://doi.org/10.3390/app13148504
[13]	Diego Fernando and Arlex Chaves, “Decoupled solution of the sediment transport and 2D shallow water equations using the finite volume method”, Results in Engineering 15 (2022) 100504. https://doi.org/10.1016/j.rineng.2022.100504
[14]	Xiyan Yang and Shanghong Zhang, “Implementation of a Local Time Stepping Algorithm and Its Acceleration Effect on Two-Dimensional Hydrodynamic Models”, Water 2020, 12, 1148. https://doi.org/ 10.3390/w12041148
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[16]	Miguel Masó and Alessandro Franci, “A Lagrangian-Eulerian procedure for the coupled solution of the Navier-Stokes and shallow water equations for landslide-generated waves”, Advanced Modeling and Simulation in Engineering Sciences (2022). https://doi.org/10.1186/s40323-022-00225-9

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APA Style

Ri, M. C., Jang, I. (2025). Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. American Journal of Mechanical and Industrial Engineering, 10(5), 96-100. https://doi.org/10.11648/j.ajmie.20251005.12

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ACS Style

Ri, M. C.; Jang, I. Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. Am. J. Mech. Ind. Eng. 2025, 10(5), 96-100. doi: 10.11648/j.ajmie.20251005.12

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AMA Style

Ri MC, Jang I. Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. Am J Mech Ind Eng. 2025;10(5):96-100. doi: 10.11648/j.ajmie.20251005.12

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@article{10.11648/j.ajmie.20251005.12,
  author = {Myong Chol Ri and Il Jang},
  title = {Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows
},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {10},
  number = {5},
  pages = {96-100},
  doi = {10.11648/j.ajmie.20251005.12},
  url = {https://doi.org/10.11648/j.ajmie.20251005.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20251005.12},
  abstract = {Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.
},
 year = {2025}
}

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TY  - JOUR
T1  - Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows

AU  - Myong Chol Ri
AU  - Il Jang
Y1  - 2025/11/26
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmie.20251005.12
DO  - 10.11648/j.ajmie.20251005.12
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 96
EP  - 100
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20251005.12
AB  - Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.

VL  - 10
IS  - 5
ER  -

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Author Information

Myong Chol Ri

Faculty of Physical Engineering, Kim Chaek University of Technology, Pyongyang, DPR Korea

Contact Email

http://orcid.org/0009-0007-5835-904X
Il Jang

Faculty of Physical Engineering, Kim Chaek University of Technology, Pyongyang, DPR Korea

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APA Style

Ri, M. C., Jang, I. (2025). Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. American Journal of Mechanical and Industrial Engineering, 10(5), 96-100. https://doi.org/10.11648/j.ajmie.20251005.12

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ACS Style

Ri, M. C.; Jang, I. Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. Am. J. Mech. Ind. Eng. 2025, 10(5), 96-100. doi: 10.11648/j.ajmie.20251005.12

Copy | Download

AMA Style

Ri MC, Jang I. Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows. Am J Mech Ind Eng. 2025;10(5):96-100. doi: 10.11648/j.ajmie.20251005.12

Copy | Download

@article{10.11648/j.ajmie.20251005.12,
  author = {Myong Chol Ri and Il Jang},
  title = {Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows
},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {10},
  number = {5},
  pages = {96-100},
  doi = {10.11648/j.ajmie.20251005.12},
  url = {https://doi.org/10.11648/j.ajmie.20251005.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20251005.12},
  abstract = {Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Local Time Stepping Scheme Using Structured Grids for Modelling of Shallow Water Flows

AU  - Myong Chol Ri
AU  - Il Jang
Y1  - 2025/11/26
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmie.20251005.12
DO  - 10.11648/j.ajmie.20251005.12
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 96
EP  - 100
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20251005.12
AB  - Numerical simulations of shallow water flows are widely used to predict global flows such as flood flows in the sea, river and reservoir flows, especially floods due to heavy rainfall and dam break. In particular, reducing the simulation time by applying the Local Time Stepping (LTS) scheme is one way to improve the practical efficiency of numerical simulation. In this paper, we proposed LTS scheme using a structured grid for the numerical simulation of shallow water system. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. The LTS scheme is applied to shallow water flow problems with tsunami reflection pattern and its accuracy and efficiency are compared with the traditional global time step (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 59-67% CPU time reduction when compared to the GTS method. The proposed LTS scheme accurately reflects time varying water regimes and reflected waves in shallow water flows and can be used for numerical simulations of the three-dimensional shallow water flows with arbitrary topography to reduce the simulation time significantly.

VL  - 10
IS  - 5
ER  -

Copy | Download