AIRPOLL: Mathematical Modelling and Advanced Numerical Algorithms
for Simulation of Air and Water Pollution

1. Construction of positivity-preserving (monotone) schemes
2. Derivation of discrete artificial boundary conditions
3. Optimal location of industrial enterprise and
4. Optimizations of emissions from enterprises for ensuring sanitary environment criteria

Summary

The main goal of the present project is to derive and analyze new numerical schemes for the simulation of the transport and diffusion of pollutants in the atmosphere or in water. This process can be described by an advection diffusion equation in 3D. However, some simple models of environmental problems can be reduced to a one-dimensional form, e.g. saline and alum intrusion in rivers and canals, air pollution generated by a point source and air quality modelling (ozone, acid rain).

Numerical methods will be constructed for the multi-dimensional problems by reducing them to a sequence of one-dimensional problems. Moreover, these schemes must preserve important features of the continuous model, such as the positivity of the solution (monotone schemes). These specially designed difference schemes must be accompanied with artificial boundary conditions to limit the computational domain. Finally, these boundary condition are designed on a discrete level directly for the chosen scheme in order to conserve the monotonicity property and to prevent any unphysical reflection at these boundaries (cf. [DaEh]).

In a second task [DEGD] we consider the problems of optimal location of industrial enterprises and optimization of emissions from enterprises for ensuring sanitary environment criteria. Moreover, we study the problem of determination of the coefficients of diffusion and the coefficient of transformation of aerosols. This mathematical study is about how to achieve the growth of enterprise in an environmentally friendly manner (i.e. compatible with environmental protection) since overuse of resources can result in a larger release of pollution into the environment. This environmental problem is especially interesting for fast developing countries, like Vietnam but it is certainly affecting all other regions of the globe.

German team:

• Matthias Ehrhardt

Vietnamese team:

• Dang Quang A

German institutions:

• Institute of Mathematics, Technical University Berlin
• DFG Research Center Mathematics for key technologies

Vietnamese institutions:

• Institute of Information Technology, Hanoi
  • Department of Mathematical Methods for Information Technology
• Vietnamese Academy of Science and Technology (VAST)

Publications of the Project

[DaEh]	Dang Quang A and M. Ehrhardt,
	Adequate Numerical Solution of Air Pollution problems by Positive Difference schemes on unbounded domains, Math. Comput. Modelling, Vol. 44, Issue 9-10, (2006), 834-856.
[DEGD]	Dang Quang A, M. Ehrhardt, Gia Lich Tran and Duc Le,
	On the numerical solution of some problems of environmental pollution, Chapter 8 in: C.B. Bodine (ed.), Air Pollution Research Trends, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2007, pp. 171-200.
[DEGD2]	Dang Quang A, M. Ehrhardt, Gia Lich Tran and Duc Le,
	On the numerical solution of some problems of environmental pollution, Chapter 6 in: P. Robinson and R.  Gallo (ed.), Environmental Chemistry Research Progress, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2009, pp. 199-228.
[EGJ]	M. Ehrhardt, M. Günther and B.  Jacob,
	RD3 Modeling and Numerical Simulation, in: R. Koppmann (ed.), Springer Briefs on Air Quality - Climate Interaction, Springer Verlag, 2013.

ehrhardt@math.uni-wuppertal.de