Numerical methods for two-dimensional parabolic inverse problem with energy overspecification

2001 ◽  
Vol 77 (3) ◽  
pp. 441-455 ◽  
Author(s):  
Mehdi Dehghan
2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.


Author(s):  
Anna Glotko ◽  
Vitalii Belikov ◽  
Natalia Borisova ◽  
Ekaterina Vasil`eva ◽  
Aleksey Rumjancev

Introduction. A problem area of the Volga river between the Nizhny Novgorod hydroelectric power station and the city of Nizhny Novgorod has been surveyed, where unfavourable conditions for navigation, power generation, and safe living in the downstream are formed as a result of the landing level. The only solution to the problem is construction of a low-head hydraulic system (NNGU) that will reduce intensity of relief re-formations in the downstream of the Nizhny Novgorod hydraulic system and stop lowering of the bottom and level marks in this area. Purpose of this research is to study processes that occur upstream and downstream from the site of the facility to identify hazardous trends and develop practical solutions to minimize negative impacts; as well as a review of mathematical models conducted in this area for improving navigation conditions. Materials and methods. Materials of previous researches on this subject, pre-design engineering surveys and layout drawings of the designed hydraulic system are used. The researches have been performed with numerical methods using Stream 2D software package that is based on the two-dimensional differential equation Saint-Venant system. Options for low-flow conditions are considered, taking into account passing of the Nizhny Novgorod hydroelectric power station, as well as rare floods. Results. Plans for distribution of velocity modules and vectors are created, which show that construction of the low-pressure hydraulic system results in decrease in slopes and velocities of water in the problem area of the Volga-Kama cascade, as a result of which intensity of bottom deformations decreases. Rare flow passage demonstrated that difference in pools is insignificant, while, at the same time, flow of water along the left-bank floodplain passes more than believed before. Calculations of low-flow conditions demonstrated a number of deficiencies in the design, which are associated with insufficient throughput and uneven distribution of flow rates in the discharge area of the waterfront. Conclusion The results demonstrated a practical importance of using mathematical simulation with numerical methods in a two-dimensional formulation, which allow us to consider processes in more detailed manner and change the hydraulic system design in a timely manner.


Sign in / Sign up

Export Citation Format

Share Document