DOI: https://doi.org/10.26089/NumMet.v16r332

Comparison of computational efficiency of explicit and implicit schemes for the sediment transport problem in coastal zones

Authors

  • A.I. Sukhinov
  • E.A. Protsenko
  • A.E. Chistyakov
  • S.A. Shreter

Keywords:

mathematical model
sediment transport
distributed computing
parallel programming
dynamics of marine sediments
shallow water equations
diffusion-convection-reaction equation

Abstract

An unsteady spatial two-dimensional sediment transport model in coastal zones is considered. The model takes into account the following physical parameters and processes: the soil porosity; the critical shear stress at which the sediment displacement begins; the turbulent exchange; the dynamically variable geometry of the bottom and the level elevation function; the wind flows; and the bottom friction. A spatial three-dimensional hydrodynamic model for coastal zones and a transport model for suspended particles are proposed and implemented on a computing cluster. Some numerical results are discussed.

New computational technologies

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Published

2015-06-18

Issue

Vol. 16 (2015): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.I. Sukhinov

A.P. Chekhov Taganrog Institute
• Dean, Professor

E.A. Protsenko

A.P. Chekhov Taganrog Institute
• Associate Professor

A.E. Chistyakov

Kalyaev Research Institute of Multiprocessor Computing Systems
• Associate Professor

S.A. Shreter

A.P. Chekhov Taganrog Institute
• Senior Lecturer

References

  1. I. O. Leont’ev, Coastal Dynamics: Waves, Currents, Deposit Fluxes (GEOS, Moscow, 2001) [in Russian].
  2. E. A. Protsenko, “Model and Algorithms of the Sediment Transport Problem Solution,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 8, 71-75 (2009).
  3. E. A. Protsenko, “A Two-Dimensional Finite-Difference Model for the Formation of Sediments in a Coastal Zone and Its Software Implementation,” Inzh. Vestn. Dona, No. 3, 23-31 (2010).
  4. A. I. Sukhinov, A. E. Chistyakov, and E. A. Protsenko, “Mathematical Modeling of Sediment Transport in the Coastal Zone of Shallow Reservoirs,” Mat. Model. 25 (12), 65-82 (2013). [Math. Models Comput. Simul. 6 (4), 351-363 (2014)].
  5. A. I. Sukhinov, A. E. Chistyakov, and E. A. Protsenko, “Sediment Transport Mathematical Modeling in a Coastal Zone Using Multiprocessor Computing Systems,” Vychisl. Metody Programm. 15, 610-620 (2014).
  6. T. Ezer and G. L. Mellor, “Sensitivity Studies with the North Atlantic Sigma Coordinate Princeton Ocean Model,” Dyn. Atmos. Oceans 32 (3-4), 155-208 (2000).
  7. E. E. Degtyareva, E. A. Protsenko, and A. E. Chistyakov, “Software Implementation of a Three-Dimensional Model of Sediment Transport in Shallow Waters,” Inzh. Vestn. Dona, No. 4, 30-32 (2012).
  8. E. E. Degtyareva and A. E. Chistyakov, “Modeling Sediment Transport Based on Experimental Studies in Azov Sea,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 2, 112-118 (2012).
  9. A. I. Sukhinov, A. V. Nikitina, A. E. Chistyakov, and I. S. Semenov, “Mathematical Modeling of the Formation of Suffocation Conditions in Shallow Basins Using Multiprocessor Computing Systems,” Vychisl. Metody Programm. 14, 103-112 (2013).
  10. A. I. Sukhinov and A. V. Nikitina, “Mathematical Modelling and Expeditional Investigations of Water Quality in Azov Sea,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 8, 62-73 (2011).
  11. A. I. Sukhinov, A. E. Chistyakov, and N. A. Fomenko, “Method of Construction of Difference Scheme for Problems of Diffusion-Convection-Reaction with Taking into Account the Degree of Filling the Control Volume,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 4, 87-98 (2013).
  12. A. I. Sukhinov, A. E. Chistyakov, and E. V. Alekseenko, “Numerical Realization of the Three-Dimensional Model of Hydrodynamics for Shallow Water Basins on a High-Performance System,” Mat. Model. 23 (3), 3-21 (2011) [Math. Models Comput. Simul. 3 (5), 562-574 (2011)].
  13. V. S. Vasil’ev and A. I. Sukhinov, “Precise Two-Dimensional Models for Shallow Water Basins,” Mat. Model. 15 (10), 17-34 (2003).
  14. A. I. Sukhinov, A. E. Chistyakov, E. F. Timofeeva, and A. V. Shishenya, “Mathematical Model for Calculating Coastal Wave Processes,” Mat. Model. 24 (8), 32-44 (2012) [Math. Models Comput. Simul. 5 (2), 122-129 (2013)].
  15. A. E. Chistyakov, “About Approximation of Boundary Conditions of a Three-Dimensional Model of Aquatic Environment Motion,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 6, 66-77 (2010).
  16. B. N. Chetverushkin, “Resolution Limits of Continuous Media Models and Their Mathematical Formulations,” Mat. Model. 24 (11), 33-52 (2012) [Math. Models Comput. Simul. 5 (3), 266-279 (2012)].
  17. A. I. Sukhinov, A. E. Chistyakov, and A. V. Shishenya, “Error Estimate for Diffusion Equations Solved by Schemes with Weights,” Mat. Model. 25 (11), 53-64 (2013) [Math. Models Comput. Simul. 6 (3), 324-331 (2014)].
  18. A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, 2001).
  19. A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations (Nauka, Moscow, 1978; Birkh854user, Basel, 1989).
  20. A. N. Konovalov, “The Steepest Descent Method with an Adaptive Alternating-Triangular Preconditioner,” Differ. Uravn. 40 (7), 953-963 (2004) [Differ. Equ. 40 (7), 1018-1028 (2004)].
  21. A. N. Konovalov, “To the Theory of the Alternating Triangle Iteration Method,” Sib. Mat. Zh. 43 (3), 552-572 (2002) [Sib. Math. J. 43 (3), 439-457 (2002)].
  22. A. I. Sukhinov and A. E. Chistyakov, “Adaptive Modified Alternating Triangular Iterative Method for Solving Grid Equations with a Non-Self-Adjoint Operator,” Mat. Model. 24 (1), 3-20 (2012) [Math. Models Comput. Simul. 4 (4), 398-409 (2012)].
  23. A. E. Chistyakov, “Speedup and Efficiency Estimation of Parallel SSOR Algorithm,” Izv. Yuzhn. Federal. Univ., Tekh. Nauki, No. 6, 237-249 (2010).