Application of a boundary-type algorithm to the inverse problems of convective heat and mass transfer

Abstract

The inverse problems of the convection-diffusion equation (ICDE) have received extensive attention in incomplete boundary conditions and uncertain source terms. They can be applied in thermally stratified pipe elbows and so on. Many algorithms need to combine with optimization algorithms to repeatedly calculate the direct problem in the solution process. To solve such problems, this paper employs a boundary-type algorithm named the half-boundary method (HBM). The HBM does not require additional repeated optimization of the direct problem. To test the performance of the method, the numerical simulations of some problems have been carried out, including the inverse problems of heat convection, river pollution and air pollution. The results show that the HBM has the desired accuracy by comparing with the exact solution. If there are errors in the measurement process, the solution doesn't generate a large deviation from the result. It is worth noting that the placement of internal measurement points minimally impacts the numerical results within the solution domain. And the method is also able to handle with discontinuous problems. Because the Gaussian plume model verifies the accuracy of HBM, the HBM can quickly calculate the atmospheric diffusion of the non-Gaussian plume model.