Das Projekt "AIRPOLL: Mathematical Modelling and Advanced Numerical Algorithms for Simulation of Air and Water Pollution - Bilateral German-Vietnamese Initiation Project mathematics in environmental sciences" wird vom Umweltbundesamt gefördert und von Universität Wuppertal, Fachgruppe Mathematik und Informatik, Arbeitsgruppe Angewandte Mathematik: Numerische Analysis durchgeführt. 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.