Research On The Inverse Problem Of Two Types Of Low Dimensional Fluid Transfer Processes

Any scientific problem has three elements: input,output,and system conditions.According to the logical relationship between the three elements,scientific problems can be divided into direct problems,reconstruction problems,and identification problems.The reconstruction problem and the identification problem belong to inverse problems.Currently,research on inverse problems has penetrated into various fields.The main characteristic of inverse problems,which is different from traditional forward problems,is that most inverse problems belong to ill conditioned problems,that is,they cannot satisfy the three elements of solution existence,singularity,and numerical stability when solving inverse problems.This paper focuses on the inverse problem of determining initial conditions and system identification.The identification problem in the inverse problem is to deduce the system parameters based on the input and output conditions of the system.This paper takes a typical one-dimensional pipe network leakage detection and leakage point location calculation as an example to study the identification problem.The specific method is to use the flow balance method to determine the leakage of the pipe network based on the phenomenon that the flow rate changes after the pipe network leakage,using the data obtained from the pressure and flow sensors arranged at the beginning and end of the pipe section as input and output conditions,the calculation of the resistance coefficient along the pipeline is simplified based on the characteristics of large flow.The relevant parameters of the pipe network are inversely deduced using Darcy’s formula,and a calculation method for the leakage location of the pipe section is given.The reconstruction problem in the inverse problem is to deduce the input conditions based on the output conditions and system parameters of the system.This paper studies the reconstruction problem using the traceability of gaseous pollutants in a closed space as an example.Based on computational fluid dynamics theory,using the indoor pollutant concentration information detected by sensors as the initial condition for the inverse problem calculation,the inverse problem modeling method is used to restore the propagation process of gaseous pollutants,thereby inferring the location of the pollution source.This paper uses a quasi-reversible method to identify the location of pollution sources.The specific method is to add a third order stable term to the pollutant propagation control equation under the Euler reference coordinate system and use a negative time step to calculate the pollutant reverse traceability process to reproduce the propagation process of gaseous pollutants.This paper analyzes the stability of the inverse problem equation with third order terms,and the results show that the third order equation is suitable for the calculation of the inverse problem of pollutant traceability.In order to verify the above method,it is applied to one-dimensional and two-dimensional models,and simulation calculations are carried out respectively considering two situations: no background flow field and background flow field.By comparing the pollution source location identified by using inverse problem calculation with the actual pollution source location,the results show that the QR inverse problem model can relatively accurately locate the pollution source.