259 research outputs found
On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond
An improved understanding of the divergence-free constraint for the
incompressible Navier--Stokes equations leads to the observation that a
semi-norm and corresponding equivalence classes of forces are fundamental for
their nonlinear dynamics. The recent concept of {\em pressure-robustness}
allows to distinguish between space discretisations that discretise these
equivalence classes appropriately or not. This contribution compares the
accuracy of pressure-robust and non-pressure-robust space discretisations for
transient high Reynolds number flows, starting from the observation that in
generalised Beltrami flows the nonlinear convection term is balanced by a
strong pressure gradient. Then, pressure-robust methods are shown to outperform
comparable non-pressure-robust space discretisations. Indeed, pressure-robust
methods of formal order are comparably accurate than non-pressure-robust
methods of formal order on coarse meshes. Investigating the material
derivative of incompressible Euler flows, it is conjectured that strong
pressure gradients are typical for non-trivial high Reynolds number flows.
Connections to vortex-dominated flows are established. Thus,
pressure-robustness appears to be a prerequisite for accurate incompressible
flow solvers at high Reynolds numbers. The arguments are supported by numerical
analysis and numerical experiments.Comment: 43 pages, 18 figures, 2 table
Simultaneous single-step one-shot optimization with unsteady PDEs
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is non-trivial. In this paper, we provide a framework that makes the single-step one-shot method applicable for unsteady PDEs that are solved by classical time-marching schemes. The one-shot method is applied to an optimal control problem with unsteady incompressible Navier-Stokes equations that are solved by an industry standard simulation code. With the Van-der-Pol oscillator as a generic model problem, the modified simulation scheme is further improved using adaptive time scales. Finally, numerical results for the advection-diffusion equation are presented. Keywords: Simultaneous optimization; One-shot method; PDE-constrained optimization; Unsteady PDE; Adaptive time scal
Index handling and assign optimization for Algorithmic Differentiation reuse index managers
For operator overloading Algorithmic Differentiation tools, the
identification of primal variables and adjoint variables is usually done via
indices. Two common schemes exist for their management and distribution. The
linear approach is easy to implement and supports memory optimization with
respect to copy statements. On the other hand, the reuse approach requires more
implementation effort but results in much smaller adjoint vectors, which are
more suitable for the vector mode of Algorithmic Differentiation. In this
paper, we present both approaches, how to implement them, and discuss their
advantages, disadvantages and properties of the resulting Algorithmic
Differentiation type. In addition, a new management scheme is presented which
supports copy optimizations and the reuse of indices, thus combining the
advantages of the other two. The implementations of all three schemes are
compared on a simple synthetic example and on a real world example using the
computational fluid dynamics solver in SU2.Comment: 20 pages, 14 figures, 4 table
Aerostructural Wing Shape Optimization assisted by Algorithmic Differentiation
With more efficient structures, last trends in aeronautics have witnessed an
increased flexibility of wings, calling for adequate design and optimization
approaches. To correctly model the coupled physics, aerostructural optimization
has progressively become more important, being nowadays performed also
considering higher-fidelity discipline methods, i.e., CFD for aerodynamics and
FEM for structures. In this paper a methodology for high-fidelity
gradient-based aerostructural optimization of wings, including aerodynamic and
structural nonlinearities, is presented. The main key feature of the method is
its modularity: each discipline solver, independently employing algorithmic
differentiation for the evaluation of adjoint-based sensitivities, is
interfaced at high-level by means of a wrapper to both solve the aerostructural
primal problem and evaluate exact discrete gradients of the coupled problem.
The implemented capability, ad-hoc created to demonstrate the methodology, and
freely available within the open-source SU2 multiphysics suite, is applied to
perform aerostructural optimization of aeroelastic test cases based on the
ONERA M6 and NASA CRM wings. Single-point optimizations, employing Euler or
RANS flow models, are carried out to find wing optimal outer mold line in terms
of aerodynamic efficiency. Results remark the importance of taking into account
the aerostructural coupling when performing wing shape optimization
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