Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a level-set function

International audienceThis paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a level-set method for increasing the eciency of reactive uid ows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers ow simulations compared to the ordinary single-relaxation time model. The cost function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with dierent Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efcient for solving topology optimization problems of reactive uid ows, in dierent operating conditions