Environmental Engineering Research

Korean Society of Environmental Engineers (대한환경공학회)
권호 표지
DOI QR코드

DOI QR Code

Numerical simulation of advection-diffusion on flow in waste stabilization ponds (1-dimension) with finite difference method forward time central space scheme

  • Putri, Gitta Agnes (Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University) ;
  • Sunarsih, Sunarsih (Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University) ;
  • Hariyanto, Susilo (Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University)
  • Received : 2017.03.09
  • Accepted : 2018.04.20
  • Published : 2018.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents the numerical simulation of advection-diffusion mechanism of BOD concentration which was used as an indicator of waste only in one flow-direction of waste stabilization ponds (1-dimension (1-D)). This model was represented in partial differential equation order 2. The purpose of this paper was to determine the simulation of the model 1-D of wastewater transport phenomena based advection-diffusion mechanism and did validate the model. Numerical methods which was used for the solution of this model is finite difference method with Forward Time Central Space scheme. The simulation results which was obtained would be compared with field observation data as a validation model. Collection of field data was carried out in the Wastewater Treatment Plant Sewon, Bantul, D.I. Yogyakarta. The results of numerical simulations were indicate that the advection-diffusion mechanism takes place continuously over time. Then validation of the model was state that there was a difference between the calculation results with the field data, with a correlation value of 0.998.

Keywords

References

  1. Metcalf & Eddy, Inc. Wastewater engineering: Treatment disposal reuse. New York: McGraw-Hill Publishing Company; 1997.
  2. Beran B, Kargi K. A dynamic mathematical model for waste water stabilization ponds. Eco. Mod. 2005;181:39-57. https://doi.org/10.1016/j.ecolmodel.2004.06.022
  3. Kayombo S, Mbwette TSA, Katima JHY, Jorgensen SE. Effects of substrate concentrations on the growth of heterotrophic bacteria and algae in secondary facultative ponds. Water Res. 2003;37:2937-2943. https://doi.org/10.1016/S0043-1354(03)00014-9
  4. James A. An introduction to water quality modelling. England: John Wiley & Sons; 1993.
  5. Sunarsih, Purwanto, Budi WS. Mathematical modeling regime steady state for domestic wastewater treatment facultative stabilization ponds. J. Urb. Environ. Eng. 2013;7:293-301. https://doi.org/10.4090/juee.2013.v7n2.293301
  6. Mayo AW, Abbas M. Removal mechanisms of nitrogen in waste stabilization ponds. Phys. Chem. Earth. 2014;72-75:77-82. https://doi.org/10.1016/j.pce.2014.09.011
  7. Gao G, Falconer RA, Lin B. Modelling the fate and transport of faecal bacteria in estuarine and coastal waters. Mar. Pollut. Bull. 2005;100:162-168.
  8. Thongmoon M, McKibbin R, Tangmanee R. Numerical solution of a 3-D advection-dispersion model for pollutant transport. Thai J. Math. 2007;5:91-108.
  9. Rubio AD, Zalts A, Hasi CDE. Numerical solution of the advection-reaction-diffusion equation at different scales. Environ. Modell. Softw. 2008;23:90-95. https://doi.org/10.1016/j.envsoft.2007.05.009
  10. Prieto FU, Munoz JJB, Corvinos LG. Application of the generalized finite difference method to solve the advection-diffusion equation. J. Comput. Appl. Math. 2011;235:1849-1855. https://doi.org/10.1016/j.cam.2010.05.026
  11. Sousa E. A second order explicit finite difference method for the fractional advection diffusion equation. Comput. Math. Appl. 2012;64:3141-3152. https://doi.org/10.1016/j.camwa.2012.03.002
  12. Sousa E. An explicit high order method for fractional advection diffusion equations. J. Comput. Phys. 2014;278:257-274. https://doi.org/10.1016/j.jcp.2014.08.036
  13. Thongmoon M, McKibbin R. A comparison of some numerical methods for the advection-diffusion equation. Res. Lett. Inf. Math. Sci. 2006;10:49-62.
  14. Najafi HS, Hajinezhad H. Solving one-dimensional advection-dispersion with reaction using some finite-difference methods. Appl. Math. Sci. 2008;2:2611-2618.
  15. Appadu AR, Djoko JK, Gidey HH. A computational study of three numerical methods for some advection-diffusion problems. Appl. Math. Comput. 2016;272:629-647.
  16. Welty JR, Wicks CE, Wilson RE, Rorrer G. Fundamentals of momentum, heat and mass transfer. 4th Ed. New York: John Wiley & Sons; 2001.
  17. White FM. Fluid mechanics. Boston: WCB McGraw-Hi; 1998.
  18. Strauss W. Partial differential equations. United States of America: John Wiley & Sons; 2008.
  19. Subiyanto, Ahmad MF, Mamat M, Husain ML. Comparison of numerical method for forward and backward time centered space for long-term simulation of shoreline evolution. Appl. Math. Sci. 2013;7:5165-5173.
  20. Atkinson K. Elementary numerical analysis. New York: John Wiley & Sons; 1985.

Cited by

  1. Macrobiont: Cradle for the Origin of Life and Creation of a Biosphere vol.10, pp.11, 2018, https://doi.org/10.3390/life10110278