Main Article Content

Abstract

Dynamic equations of flow in a rectangular inclined channel are solved numerically for the case where the friction force of the channel wall is neglected by the gravity force. The flow discharge and the cross-section area along the channel are physical quantity that is calculated. In non-dimensional variables, the equations indicate solution in traveling wave occurring for critical flow. Near that type of flow, the perturbation method is applied to get second order equations that are first order partial differential equation with external force from the lower order equations. Numerical solution is obtained by predictor-corrector method, and the effect of these second order equations can be observed to the traveling wave, depending on the type of the flow, su-percritical or subcritical.

Keywords

Dynamic wave equation flood routing model perturbation method predictor-corrector method

Article Details

How to Cite
Wiryanto, L. H., & Widyawati, R. (2022). Numerical Simulation of Flood Routing, Model of Dynamic Equations. Journal of the Indonesian Mathematical Society, 28(2), 122–132. https://doi.org/10.22342/jims.28.2.1111.122-132

References

  1. Agiralioglu, N., ”Water routing on diverging-converging watershed”, J. Hydraul., 107 (1981), 1003-1017.
  2. Agiralioglu, N., ”Estimation of the time of concentration for diverging surface”, J. Hydrol. Sci., 33(2) (1988), 173-179.
  3. Akan, A.O., Yen, C.Y., ”Diffusion-wave flood routing in channel networks”, J. Hydraul., 107 (1981), 719-732.
  4. Gonwa, W.S., Kavvas, M.L., ”A modified diffusion equation for flood propagation in trapezoidal channels”, J. Hydrol., 83 (1986), 119-136.
  5. Ponce, V.M., Li, R.M., Simons, D.B., ”Applicability of kinematic and diffusion models”, J. Hydaul., 104 (1978), 353-360.
  6. Sinha, J., Eswaran, J.S., Bhallamudi, S.M., ”Comparison of spectral and finite difference methods for flood routing”, J. Hydraul., textbf121(2) (1978), 108-117.
  7. Amein, M., Fang, C.S., ”Implicit flood routing in natural channels”, J. Hydraul., 96 (1970), 918-926.
  8. Fread, D.L., ”Technique for implicit dynamic routing in rivers with tributaries”, Water Resource. Res., 9(4) (1973), 918-926.
  9. Koussis, A., ”An approximative dynamic flood routing methods”, Int. Symp. on Unsteady Flow in Open Channel, April 12-15th (1976).
  10. Lamberti, P., Pilati, S., ”Flood propagation models for real-time forecasting”, J. Hydrol., 175 (1996), 239-265.
  11. Lai, W., Khan, A.A., ”Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite difference method”, J. Hydro-dynamics, 30(2) (2018), 189-202.
  12. Keskin, M.E., Agiralioglu, N., ”A simplified dynamic model for flood routing in rectangular channels”, J. Hydrol., 202 (1997), 302-314, https://doi.org/10.1016/S0022-1694(97)00072-3
  13. Barati, R., Rahimi, S., Akbari, G.H., ”Analysis of dynamic wave model for flood routing in natural rivers”, Water Sci. Eng. , 5(3) (2012), 243-258, doi: 10.3882/j.issn.1674- 2370.2012.03.001.
  14. Sulistyono, B.A., Wiryanto, L.H., ”Investigation of flood routing by a dynamic wave model in trapezoidal channels”, AIP Conf. Proc., 1867 (2017), 020020, doi: 10.1063/1.4994423.
  15. Retsinis, E., Daskalaki, E., Papanicolaou, P., ”Dynamic flood wave routing in prismatic channel with hydrologic methods”, J. Water Supply: Re-search and Tech. Aqua, JWS 2019091 (2019).
  16. Sulistyono, B.A., Wiryanto, L.H., ”A staggered method for numerical flood routing in rectangular channels”, Adv. Appl. Fluid Mech., 23(2) (2019), 171-179.
  17. Stelling, G.S., Duinmeijer, S.P.A., ”A staggered conservative scheme for every Froude number in rapidly varied shallow water flows”, Int. J. Nu-mer. methods Fluids, 43912 (2003), 1329- 1354, doi: 10.1001/fld.537.
  18. Mungkasi, S., Magdalena, I., Pudjaprasetya, S.R., Wiryanto, L.H., Robert, S.G., ”A staggered method for the shallow water equations involv-ingvarying channel width an topography”, Int. J. Multiscale Comp. Eng., 16 (3) (2018), 231-244.
  19. Sulistyono, B.A., Wiryanto, L.H., Mungkasi, S., ”A staggered method for simulating shallow water flows along channels with irregular geometry and friction”, Int. J. Adv. Sci. Eng. Inf. Tech., 10 (3) (2020), 952-958.
  20. Wiryanto, L.H., Mungkasi, S., ”Numerical solution of wave generated by flow over a bump”, Far East J. Math. Sci., 100(10) (2016), 1717-1726.
  21. Wiryanto, L.H., Mungkasi, S., ”Analytical solution of Boussinesq equations as a model of wave generation”, AIP Conf. Proc., 1707, 050020-1 (2016b), doi: 10.1063/1.4940852.
  22. Tuck, E.O., Wiryanto, L.H., ”On steady periodic interfacial waves”, J. Eng. Math., 35 (1999),71-84.
  23. Wiryanto, L.H., ”Wave propagation passing over a submerged porous breakwater,” J. Eng. Math., 70 (2011),129-136, doi: 10.1007/s10665-010-9419-3.
  24. Cunge, J.A, Holly, F.M., Verwey, A. Jr., Practical aspects of computational river hydraulics, Pitman, Advanced Publishing Program (1980)

Most read articles by the same author(s)