Parts of the adjoint optimisation library were re-designed to generalise
the way sensitivity derivatives (SDs) are computed and to allow easier
extension to primal problems other than the ones governed by
incompressible flows. In specific:
- the adjoint solver now holds virtual functions returning the part of
SDs that depends only on the primal and the adjoint fields.
- a new class named designVariables was introduced which, apart from
defining the design variables of the optimisation problem and
providing hooks for updating them in an optimisation loop, provides
the part of the SDs that affects directly the flow residuals (e.g.
geometric variations in shape optimisation, derivatives of source
terms in topology optimisation, etc). The final assembly of the SDs
happens here, with the updated sensitivity class acting as an
intermediate.
With the new structure, when the primal problem changes (for instance,
passive scalars are included), the same design variables and sensitivity
classes can be re-used for all physics, with additional contributions to
the SDs being limited (and contained) to the new adjoint solver to be
implemented. The old code structure would require new SD classes for
each additional primal problem.
As a side-effect, setting up a case has arguably become a bit easier and
more intuitive.
Additional changes include:
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- Changes in the formulation and computation of shape sensitivity derivatives
using the E-SI approach. The latter is now derived directly from the
FI approach, with proper discretization for the terms and boundary
conditions that emerge from applying the Gauss divergence theorem used
to transition from FI to E-SI. When E-SI and FI are based on the same
Laplace grid displacement model, they are now numerically equivalent
(the previous formulation proved the theoretical equivalence of the
two approaches but numerical results could differ, depending on the
case).
- Sensitivity maps at faces are now computed based (and are deriving
from) sensitivity maps at points, with a constistent point-to-face
interpolation (requires the differentiation of volPointInterpolation).
- The objective class now allocates only the member pointers that
correspond to the non-zero derivatives of the objective w.r.t. the
flow and geometric quantities, leading to a reduced memory footprint.
Additionally, contributions from volume-based objectives to the
adjoint equations have been re-worked, removing the need for
objectiveManager to be virtual.
- In constrained optimisation, an adjoint solver needs to be present for
each constraint function. For geometric constraints though, no adjoint
equations need to solved. This is now accounted for through the null
adjoint solver and the geometric objectives which do not allocate
adjoint fields for this kind of constraints, reducing memory
requirements and file clutter.
- Refactoring of the updateMethod to collaborate with the new
designVariables. Additionally, all updateMethods can now read and
write restart data in binary, facilitating exact continuation.
Furthermore, code shared by various quasi-Newton methods (BFGS, DBFGS,
LBFGS, SR1) has been organised in the namesake class. Over and above,
an SQP variant capable of tackling inequality constraints has been
added (ISQP, with I indicating that the QP problem in the presence of
inequality constraints is solved through an interior point method).
Inequality constraints can be one-sided (constraint < upper-value)
or double-sided (lower-value < constraint < upper-value).
- Bounds can now be defined for the design variables.
For volumetricBSplines in specific, these can be computed as the
mid-points of the control points and their neighbouring ones. This
usually leads to better-defined optimisation problems and reduces the
chances of an invalid mesh during optimisation.
- Convergence criteria can now be defined for the optimisation loop
which will stop if the relative objective function reduction over
the last objective value is lower than a given threshold and
constraints are satisfied within a give tolerance. If no criteria are
defined, the optimisation will run for the max. given number of cycles
provided in controlDict.
- Added a new grid displacement method based on the p-Laplacian
equation, which seems to outperform other PDE-based approaches.
TUT: updated the shape optimisation tutorials and added a new one
showcasing the use of double-sided constraints, ISQP, applying
no-overlapping constraints to volumetric B-Splines control points
and defining convergence criteria for the optimisation loop.
The adjoint library is enhanced with new functionality enabling
automated shape optimisation loops. A parameterisation scheme based on
volumetric B-Splines is introduced, the control points of which act as
the design variables in the optimisation loop [1, 2]. The control
points of the volumetric B-Splines boxes can be defined in either
Cartesian or cylindrical coordinates.
The entire loop (solution of the flow and adjoint equations, computation
of sensitivity derivatives, update of the design variables and mesh) is
run within adjointOptimisationFoam. A number of methods to update the
design variables are implemented, including popular Quasi-Newton methods
like BFGS and methods capable of handling constraints like loop using
the SQP or constraint projection.
The software was developed by PCOpt/NTUA and FOSS GP, with contributions from
Dr. Evangelos Papoutsis-Kiachagias,
Konstantinos Gkaragounis,
Professor Kyriakos Giannakoglou,
Andy Heather
[1] E.M. Papoutsis-Kiachagias, N. Magoulas, J. Mueller, C. Othmer,
K.C. Giannakoglou: 'Noise Reduction in Car Aerodynamics using a
Surrogate Objective Function and the Continuous Adjoint Method with
Wall Functions', Computers & Fluids, 122:223-232, 2015
[2] E. M. Papoutsis-Kiachagias, V. G. Asouti, K. C. Giannakoglou,
K. Gkagkas, S. Shimokawa, E. Itakura: ‘Multi-point aerodynamic shape
optimization of cars based on continuous adjoint’, Structural and
Multidisciplinary Optimization, 59(2):675–694, 2019
A set of libraries and executables creating a workflow for performing
gradient-based optimisation loops. The main executable (adjointOptimisationFoam)
solves the flow (primal) equations, followed by the adjoint equations and,
eventually, the computation of sensitivity derivatives.
Current functionality supports the solution of the adjoint equations for
incompressible turbulent flows, including the adjoint to the Spalart-Allmaras
turbulence model and the adjoint to the nutUSpaldingWallFunction, [1], [2].
Sensitivity derivatives are computed with respect to the normal displacement of
boundary wall nodes/faces (the so-called sensitivity maps) following the
Enhanced Surface Integrals (E-SI) formulation, [3].
The software was developed by PCOpt/NTUA and FOSS GP, with contributions from
Dr. Evangelos Papoutsis-Kiachagias,
Konstantinos Gkaragounis,
Professor Kyriakos Giannakoglou,
Andy Heather
and contributions in earlier version from
Dr. Ioannis Kavvadias,
Dr. Alexandros Zymaris,
Dr. Dimitrios Papadimitriou
[1] A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, and C. Othmer.
Continuous adjoint approach to the Spalart-Allmaras turbulence model for
incompressible flows. Computers & Fluids, 38(8):1528–1538, 2009.
[2] E.M. Papoutsis-Kiachagias and K.C. Giannakoglou. Continuous adjoint methods
for turbulent flows, applied to shape and topology optimization: Industrial
applications. 23(2):255–299, 2016.
[3] I.S. Kavvadias, E.M. Papoutsis-Kiachagias, and K.C. Giannakoglou. On the
proper treatment of grid sensitivities in continuous adjoint methods for shape
optimization. Journal of Computational Physics, 301:1–18, 2015.
Integration into the official OpenFOAM release by OpenCFD
