Transient Source Terms Estimate in Advection-Diffusion Problems Using the Method of Fundamental Solutions and an Eulerian-Lagrangian Transformation

Abstract

In this work, transient source terms in advection-diffusion problems are recovered. The solution technique proposed relies on the implicit finite difference method coupled with the method of fundamental solutions, a technique for solving partial differential equations when their fundamental solution is known. The Truncated Singular Value Decomposition was used to overcome the ill-conditioned resulting linear system. The advection-diffusion inverse problem was solved using a Eulerian–Lagrangian method. Several numerical examples were considered for testing purposes by using simulated measurements perturbed with a Gaussian random noise for different Reynolds numbers. Results show that the proposed method provides stable and accurate estimates for the source term.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially funded by CNPq and CAPES (agencies for the fostering of science from the Brazilian Ministry of Science and Education, respectively), FAPERJ (agency for fostering of science from the Rio de Janeiro State), ANP/PRH8 (Brazilian National Agency of Oil, Gas and Biofuels), and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Finance Code 001.

Notes on contributors

Gustavo R. Gasperazzo

Gustavo R. Gasperazzo completed his Master thesis under the supervision of Prof. Marcelo José Colaço at Federal University of Rio de Janeiro, Brazil, in 2022. He received his degree in mechanical engineering from Federal Institute of Espírito Santo in 2020 and in mechanical and armament engineering from Military Institute of Engineering in 2022. He works with thermo-fluid modeling, inverse heat transfer and optimization. He is currently an officer in the Brazilian Army working in the field of mechanical and armament engineering.

Marcelo J. Colaço

Marcelo J. Colaço graduated in Mechanical Engineering in 1996 and received his Ph.D. in 2001 all from the Department of Mechanical Engineering at the Federal University of Rio de Janeiro (UFRJ). He was promoted to Associate Professor in 2004, and full professor in 2017 at the Department of Mechanical Engineering of the UFRJ. His research activity, both numerical and experimental, is focused mainly on thermodynamics and fluid mechanics problems. He has developed optimization techniques, algorithm and solution methods for inverse heat transfer problems and has published scientific articles in the most important international journals related to inverse problems as well as heat and mass transfer and computational fluid dynamics. He has also been a visiting professor at University of Parma since 2020.