
-
Previous Article
Darcy-Forchheimer relation in Magnetohydrodynamic Jeffrey nanofluid flow over stretching surface
- DCDS-S Home
- This Issue
-
Next Article
Numerical investigation of space fractional order diffusion equation by the Chebyshev collocation method of the fourth kind and compact finite difference scheme
Self-adaptive algorithm based on a posteriori analysis of the error applied to air quality forecasting using the finite volume method
1. | MAE2D laboratory, University Abdelmalek Essaadi, Polydisciplinary Faculty of Larache, Road of Rabat, Larache, Morocco |
2. | National Meteorological Direction of Morocco, Airport Casa-Anfa, Casa Oasis - Casablanca, Morocco |
In this work, we present a self-adaptive algorithm based on the techniques of the a posteriori estimates for the transport equation modeling the dispersion of pollutants in the atmospheric boundary layer at the local scale (industrial accident, urban air quality). The goal is to provide a powerful model for forecasting pollutants concentrations with better manipulation of available computing resources.
This analysis is based on a vertex-centered Finite Volume Method in space and an implicit Euler scheme in time. We apply and validate our model, using a self-adaptive algorithm, with real atmospheric data of the Grand Casablanca area (Morocco).
References:
[1] |
M. Afif, A. Bergam, Z. Mghazli and R. Verfurth,
A posteriori estimators of the finite volume discretization of an elliptic problem, Numer. Algorithms, 34 (2003), 127-136.
doi: 10.1023/B:NUMA.0000005400.45852.f3. |
[2] |
B. Amaziane, A. Bergam, M. El Ossmani and Z. Mghazli,
A posteriori estimators for vertex centred finite volume discretization of a convection-diffusion-reaction equation arising in flow in porous media, Internat. J. Numer. Methods Fluids, 59 (2009), 259-284.
doi: 10.1002/fld.1456. |
[3] |
A. Bergam, C. Bernardi, F. Hecht and Z. Mghazli,
Error indicators for the mortar finite element discretization of a parabolic problem, Numer. Algorithms, 34 (2003), 187-201.
doi: 10.1023/B:NUMA.0000005362.95126.4c. |
[4] |
A. Bergam, Z. Mghazli and R. Verfürth,
Estimations a posteriori d'un schéma de volumes finis pour un problème non linéaire, Numer. Math., 95 (2003), 599-624.
doi: 10.1007/s00211-003-0460-2. |
[5] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[6] |
W. Gong and H.-R. Cho,
A numerical scheme for the integration of the gas-phase chemical rate equations in 3d atmospheric models, Atmospheric Environment, 27 (1993), 2147-2160.
doi: 10.1016/0960-1686(93)90044-Y. |
[7] |
J.-F. Louis,
A parametric model of vertical eddy fluxes in the atmosphere, Boundary-Layer Meteorology, 17 (1979), 187-202.
doi: 10.1007/BF00117978. |
[8] |
V. Mallet, A. Pourchet, D. Quélo and B. Sportisse,
Investigation of some numerical issues in a chemistry-transport model: Gas-phase simulations, J. Geophysical Research, 112 (2007), 301-317.
doi: 10.1029/2006JD008373. |
[9] |
V. Mallet and B. Sportisse,
3-D chemistry-transport model Polair: Numerical issues, validation and automatic-differentiation strategy, Atmos. Chem. Phys. Discuss., 4 (2004), 1371-1392.
doi: 10.5194/acpd-4-1371-2004. |
[10] |
V. Mallet and B. Sportisse,
Uncertainty in a chemistry-transport model due to physical parameterizations and numerical approximations: An ensemble approach applied to ozone modeling, J. Geophys. Res., 111 (2006), 1-15.
doi: 10.1029/2005JD006149. |
[11] |
W. R. Stockwell, F. Kirchner, M. Kuhn and S. Seefeld, A new mechanism for regional atmospheric chemistry modeling, J. Geophys. Res., 102 (1997).
doi: 10.1029/97JD00849. |
[12] |
W. R. Stockwell, P. Middleton, J. S. Chang and X. Tang,
The second generation regional acid deposition model chemical mechanism for regional air quality modeling, J. Geophys. Res., 95 (1990), 343-367.
doi: 10.1029/JD095iD10p16343. |
[13] |
R. B. Stull, An Introduction to Boundary Layer Meteorology, Atmospheric Sciences Library, 13, Springer, Dordrecht, 1998.
doi: 10.1007/978-94-009-3027-8. |
[14] |
World Helth Organization, Ambient Air Pollution: Pollutants, WHO Report, WHO Library Cataloguing-in-Publication Data, 2018. Available from: http://www.who.int/airpollution/ambient/pollutants/en/. Google Scholar |
[15] |
L. Wu, V. Mallet, M. Bocquet and B. Sportisse,
A comparison study of data assimilation algorithms for ozone forecasts, J. Geophys. Res., 113 (2008), 1-17.
doi: 10.1029/2008JD009991. |
show all references
References:
[1] |
M. Afif, A. Bergam, Z. Mghazli and R. Verfurth,
A posteriori estimators of the finite volume discretization of an elliptic problem, Numer. Algorithms, 34 (2003), 127-136.
doi: 10.1023/B:NUMA.0000005400.45852.f3. |
[2] |
B. Amaziane, A. Bergam, M. El Ossmani and Z. Mghazli,
A posteriori estimators for vertex centred finite volume discretization of a convection-diffusion-reaction equation arising in flow in porous media, Internat. J. Numer. Methods Fluids, 59 (2009), 259-284.
doi: 10.1002/fld.1456. |
[3] |
A. Bergam, C. Bernardi, F. Hecht and Z. Mghazli,
Error indicators for the mortar finite element discretization of a parabolic problem, Numer. Algorithms, 34 (2003), 187-201.
doi: 10.1023/B:NUMA.0000005362.95126.4c. |
[4] |
A. Bergam, Z. Mghazli and R. Verfürth,
Estimations a posteriori d'un schéma de volumes finis pour un problème non linéaire, Numer. Math., 95 (2003), 599-624.
doi: 10.1007/s00211-003-0460-2. |
[5] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58090-1. |
[6] |
W. Gong and H.-R. Cho,
A numerical scheme for the integration of the gas-phase chemical rate equations in 3d atmospheric models, Atmospheric Environment, 27 (1993), 2147-2160.
doi: 10.1016/0960-1686(93)90044-Y. |
[7] |
J.-F. Louis,
A parametric model of vertical eddy fluxes in the atmosphere, Boundary-Layer Meteorology, 17 (1979), 187-202.
doi: 10.1007/BF00117978. |
[8] |
V. Mallet, A. Pourchet, D. Quélo and B. Sportisse,
Investigation of some numerical issues in a chemistry-transport model: Gas-phase simulations, J. Geophysical Research, 112 (2007), 301-317.
doi: 10.1029/2006JD008373. |
[9] |
V. Mallet and B. Sportisse,
3-D chemistry-transport model Polair: Numerical issues, validation and automatic-differentiation strategy, Atmos. Chem. Phys. Discuss., 4 (2004), 1371-1392.
doi: 10.5194/acpd-4-1371-2004. |
[10] |
V. Mallet and B. Sportisse,
Uncertainty in a chemistry-transport model due to physical parameterizations and numerical approximations: An ensemble approach applied to ozone modeling, J. Geophys. Res., 111 (2006), 1-15.
doi: 10.1029/2005JD006149. |
[11] |
W. R. Stockwell, F. Kirchner, M. Kuhn and S. Seefeld, A new mechanism for regional atmospheric chemistry modeling, J. Geophys. Res., 102 (1997).
doi: 10.1029/97JD00849. |
[12] |
W. R. Stockwell, P. Middleton, J. S. Chang and X. Tang,
The second generation regional acid deposition model chemical mechanism for regional air quality modeling, J. Geophys. Res., 95 (1990), 343-367.
doi: 10.1029/JD095iD10p16343. |
[13] |
R. B. Stull, An Introduction to Boundary Layer Meteorology, Atmospheric Sciences Library, 13, Springer, Dordrecht, 1998.
doi: 10.1007/978-94-009-3027-8. |
[14] |
World Helth Organization, Ambient Air Pollution: Pollutants, WHO Report, WHO Library Cataloguing-in-Publication Data, 2018. Available from: http://www.who.int/airpollution/ambient/pollutants/en/. Google Scholar |
[15] |
L. Wu, V. Mallet, M. Bocquet and B. Sportisse,
A comparison study of data assimilation algorithms for ozone forecasts, J. Geophys. Res., 113 (2008), 1-17.
doi: 10.1029/2008JD009991. |








Parameter | Signification | Value |
Diffusion coefficient | ||
Velocity vector | ||
Reaction balance | ||
Second member | ||
Initial concentration |
Parameter | Signification | Value |
Diffusion coefficient | ||
Velocity vector | ||
Reaction balance | ||
Second member | ||
Initial concentration |
Step 1: | Mesh generating and data input. |
Step 2: | Solve the discrete problem. |
Step 3: | Calculate the local error indicators. |
Step 4: | Mark mesh cells and adapt mesh. |
Step 5: | Solve the discrete problem in the new adapted mesh. |
Step 6: | if the stopping test is satisfied, go to the step 7 |
else, go to the step 3. | |
Step 7: | Interpolate solution and visualization. |
Step 1: | Mesh generating and data input. |
Step 2: | Solve the discrete problem. |
Step 3: | Calculate the local error indicators. |
Step 4: | Mark mesh cells and adapt mesh. |
Step 5: | Solve the discrete problem in the new adapted mesh. |
Step 6: | if the stopping test is satisfied, go to the step 7 |
else, go to the step 3. | |
Step 7: | Interpolate solution and visualization. |
Level | Number of | jump | residual | CPU | |
elements | indicator | indicator | time | ||
primal mesh | |||||
uniform mesh |
Level | Number of | jump | residual | CPU | |
elements | indicator | indicator | time | ||
primal mesh | |||||
uniform mesh |
Level | Number of | Jump | Residual | CPU | |
elements | indicator | indicator | time | ||
Primal mesh | |||||
Adaptive mesh | |||||
uniform mesh |
Level | Number of | Jump | Residual | CPU | |
elements | indicator | indicator | time | ||
Primal mesh | |||||
Adaptive mesh | |||||
uniform mesh |
[1] |
Alberto Bressan, Wen Shen. A posteriori error estimates for self-similar solutions to the Euler equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 113-130. doi: 10.3934/dcds.2020168 |
[2] |
Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model. Electronic Research Archive, 2021, 29 (1) : 1735-1752. doi: 10.3934/era.2020089 |
[3] |
Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351 |
[4] |
Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020340 |
[5] |
Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 |
[6] |
Matúš Tibenský, Angela Handlovičová. Convergence analysis of the discrete duality finite volume scheme for the regularised Heston model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1181-1195. doi: 10.3934/dcdss.2020226 |
[7] |
Simone Fiori. Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport. Mathematical Control & Related Fields, 2021, 11 (1) : 143-167. doi: 10.3934/mcrf.2020031 |
[8] |
Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 |
[9] |
Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021012 |
[10] |
Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, 2021, 17 (2) : 827-839. doi: 10.3934/jimo.2019136 |
[11] |
Ying Liu, Yanping Chen, Yunqing Huang, Yang Wang. Two-grid method for semiconductor device problem by mixed finite element method and characteristics finite element method. Electronic Research Archive, 2021, 29 (1) : 1859-1880. doi: 10.3934/era.2020095 |
[12] |
Qiang Fu, Xin Guo, Sun Young Jeon, Eric N. Reither, Emma Zang, Kenneth C. Land. The uses and abuses of an age-period-cohort method: On the linear algebra and statistical properties of intrinsic and related estimators. Mathematical Foundations of Computing, 2020 doi: 10.3934/mfc.2021001 |
[13] |
Yue Feng, Yujie Liu, Ruishu Wang, Shangyou Zhang. A conforming discontinuous Galerkin finite element method on rectangular partitions. Electronic Research Archive, , () : -. doi: 10.3934/era.2020120 |
[14] |
Xiu Ye, Shangyou Zhang, Peng Zhu. A weak Galerkin finite element method for nonlinear conservation laws. Electronic Research Archive, 2021, 29 (1) : 1897-1923. doi: 10.3934/era.2020097 |
[15] |
Lateef Olakunle Jolaoso, Maggie Aphane. Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020178 |
[16] |
Lan Luo, Zhe Zhang, Yong Yin. Simulated annealing and genetic algorithm based method for a bi-level seru loading problem with worker assignment in seru production systems. Journal of Industrial & Management Optimization, 2021, 17 (2) : 779-803. doi: 10.3934/jimo.2019134 |
[17] |
Wenya Qi, Padmanabhan Seshaiyer, Junping Wang. A four-field mixed finite element method for Biot's consolidation problems. Electronic Research Archive, , () : -. doi: 10.3934/era.2020127 |
[18] |
Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323 |
[19] |
David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121 |
[20] |
Thomas Y. Hou, Dong Liang. Multiscale analysis for convection dominated transport equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 281-298. doi: 10.3934/dcds.2009.23.281 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]