Investigation of different time integration schemes for the 2D Shallow Water Equations on distributed memory parallel computers

1995 ◽  
Vol 3 (4-5) ◽  
pp. 287-305 ◽  
Author(s):  
Z.W. Song ◽  
D. Roose ◽  
J. Berlamont
2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.


Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2120
Author(s):  
Gnenakantanhan Coulibaly ◽  
Babacar Leye ◽  
Fowe Tazen ◽  
Lawani Adjadi Mounirou ◽  
Harouna Karambiri

Appropriate methods and tools accessibility for bi-dimensional flow simulation leads to their weak use for floods assessment and forecasting in West African countries, particularly in urban areas where huge losses of life and property are recorded. To mitigate flood risks or to elaborate flood adaptation strategies, there is a need for scientific information on flood events. This paper focuses on a numerical tool developed for urban inundation extent simulation due to extreme tropical rainfall in Ouagadougou city. Two-dimensional (2D) shallow-water equations are solved using a finite volume method with a Harten, Lax, Van Leer (HLL) numerical fluxes approach. The Digital Elevation Model provided by NASA’s Shuttle Radar Topography Mission (SRTM) was used as the main input of the model. The results have shown the capability of the numerical tool developed to simulate flow depths in natural watercourses. The sensitivity of the model to rainfall intensity and soil roughness coefficient was highlighted through flood spatial extent and water depth at the outlet of the watershed. The performance of the model was assessed through the simulation of two flood events, with satisfactory values of the Nash–Sutcliffe criterion of 0.61 and 0.69. The study is expected to be useful for flood managers and decision makers in assessing flood hazard and vulnerability.


Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.


1986 ◽  
Vol 65 (2) ◽  
pp. 253-272 ◽  
Author(s):  
L. Garcia ◽  
H.R. Hicks ◽  
B.A. Carreras ◽  
L.A. Charlton ◽  
J.A. Holmes

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