The project builds and applies modern calculation methods of the world to the construction of a water quality program that allows to calculate and simulate the process of flood propagation and substance transmission. By building a sensitive problem using optimal differential variables. The simulation model provides a theoretical method and calculation program for the gradient of the sensitivity function depending on the selected measurement location. From there, we can show that the measurement should be at the most suitable location to calculate the source of pollution emission. The main goals are written as follows:

• To find the location of pollution source through the value distribution of the gradient of the sensitivity function over the calculated domain for the inverse problem of pollution source.

• To achieve theoretical results on flow patterns, water pollution affecting domestic ecosystems in order to serve the needs of the people.

• By using current calculation methods and developing new modern mathematical methods, the topic develops better sets of calculation subroutines to improve the quality of flow simulation, improve the ability to calculate water quality.

- Theoretical results: the project presents a new correction method to find pollution         source by variable optimization method.

- Applied results: The program is calculated and tested for the test problem of the pollution water flow of Thanh Nhan lake, Hanoi.

- Scientific papers in referred journals (list):

1.1 . Thu Ha Tran, Hong Son Hoang, Hong Phong Nguyen. “A sensitivity method studying regional response to external sources of pollution and its application to 1D water pollution problem”. The 6th International Conference on Engineering Mechanics and Automation (ICEMA 2021) Hanoi, November 14, 2021. P. 144-149

1.2 . Victor Shutyaev, Tran Thu Ha, Francois-Xavier Le Dimet, Hong Son Hoang, and Nguyen Hong Phong: “On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems “, Russ. J. Numer. Anal. Math. Modelling 2022; 37(1):41–61. DOI: https://doi.org/10.1515/rnam-2022-0004.

- Technological products (describe in details: technical characteristics, place): The report summarizes the development of a research model for the 1- and 2-dimensional pollution propagation problem by building a sensitivity function that depends on the measurement location to help find the location of the pollution source. The report and Code of the calculation program are recorded at the computer of the Department of Hydrodynamics and Disaster Mitigation in the basin of the Institute of Mechanics and USB. Report on the theoretical model and calculation program on studying the problem of pollution propagation in 1 and 2 dimensions by building a sensitivity function that depends on the measurement location to help find the location of the pollution source.