AB

A. Baillet Bolivar

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A Lattice Boltzmann (LBM) solver is presented and differentiated using the discrete adjoint method. A shape optimization pipeline is implemented based on the obtained gradients. The following features are considered, aiming for applicability in industrially relevant simulation and optimization, and possible integration with a quantum LBM code in the future:

1. Recursive regularized collision operator.
2. Volumetric grid refinement with arbitrary grid geometries.
3. A mass-conserving, differentiable boundary condition for no-slip boundaries, and a methodology to deduce physical shape gradients from the bounce-back boundary condition (for integration with a quantum code).
4. Momentum inlet and pressure outlet boundary conditions.
5. Pressure-relaxation absorption region (sponge) to dampen acoustic fluctuations.
6. Coefficients of lift and drag as quantities of interest, computed with the momentum exchange method.
7. Shape parametrization with free-form deformation.

The forward solver is validated on steady and unsteady flow conditions, as are the adjoint-based gradients, which are obtained using a general methodology by Tekitek et al. [1]. The adjoint-based gradients present relative errors to finite differences of O(10⁻⁵). A steady L/D optimization case is run, presenting improvements on the base shape on the order of 20%. It is demonstrated that the adjoint methodology supports parametrization of both the collision operator and streaming matrix in a simple, extensible manner.
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