Aerodynamic design via control theory
Journal of Scientific Computing
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
Accelerated Lattice Boltzmann Schemes for Steady-State Flow Simulations
Journal of Scientific Computing
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Optimal design for non-Newtonian flows using a topology optimization approach
Computers & Mathematics with Applications
Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction
Journal of Computational Physics
Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods
Computers & Mathematics with Applications
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We study the numerical performance of a parallel Schur complement method towards the solution of the steady-state lattice Boltzmann equations on large meshes as needed for parametric design optimisation problems, in particular topology optimisation. For the gradient-based topology optimisation framework a porosity model is used to continuously transition from fluid to solid. Deriving the sensitivity equations for the lattice Boltzmann method (LBM), we identify the Jacobian of the LBM fixed-point formulation, which poses the key computational challenge in LBM topology optimisation due to its large size. We show that the Schur complement method can be used to decompose the fixed-point Jacobian, making the solution of the LBM sensitivity equations more memory efficient, in particular for 2D problems. The effectiveness of the overall lattice Boltzmann based topology optimisation framework is illustrated with the optimal design of a micro valve, posted by a dual-objective optimisation problem.