Adjoint-state Lattice Boltzmann Method: A necessary correction when cost function incorporates macroscopic quantities on boundaries
Abstract
Topology optimization of fluid flows requires the computation of the cost function gradient. Based on the partial differential equations that govern the physics, the only efficient manner to do so is using the adjoint-state method. This article highlights the property that the cost gradient is naturally not well calculated when the cost function incorporates macroscopic data at the boundary, in a LBM framework. This is due to the advection nature of Boltzmann equations which are in terms of distribution functions at the mesoscopic scale, while the cost function incorporates variables at the macroscopic scale. Two methodologies are proposed to improve the accuracy of the gradient calculation: shifting the domain of integration of the cost function and a lumping strategy. This lumping strategy has proved to constitute a substantial improvement.
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BibTeX
@article{favennec2026adjointstate,
title = {{Adjoint-state Lattice Boltzmann Method: A necessary correction when cost function incorporates macroscopic quantities on boundaries}},
author = {Yann Favennec and Mahmoud Assaf and Christophe Josset},
journal = {Computers and Fluids},
year = {2026},
month = sep,
doi = {10.1016/j.compfluid.2026.107231},
url = {https://hal.science/hal-05741095v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Adjoint-state Lattice Boltzmann Method: A necessary correction when cost function incorporates macroscopic quantities on boundaries
AU - Yann Favennec
AU - Mahmoud Assaf
AU - Christophe Josset
PY - 2026
DA - 2026/09/25
JO - Computers and Fluids
DO - 10.1016/j.compfluid.2026.107231
UR - https://hal.science/hal-05741095v1
AB - Topology optimization of fluid flows requires the computation of the cost function gradient. Based on the partial differential equations that govern the physics, the only efficient manner to do so is using the adjoint-state method. This article highlights the property that the cost gradient is naturally not well calculated when the cost function incorporates macroscopic data at the boundary, in a LBM framework. This is due to the advection nature of Boltzmann equations which are in terms of distribution functions at the mesoscopic scale, while the cost function incorporates variables at the macroscopic scale. Two methodologies are proposed to improve the accuracy of the gradient calculation: shifting the domain of integration of the cost function and a lumping strategy. This lumping strategy has proved to constitute a substantial improvement.
SN - 0045-7930
SN - 1879-0747
ER -