920 research outputs found
Adjoint-based Particle Forcing Reconstruction and Uncertainty Quantification
The forcing of particles in turbulent environments influences dynamical
properties pertinent to many fundamental applications involving particle-flow
interactions. Current study explores the determination of forcing for one-way
coupled passive particles, under the assumption that the ambient velocity
fields are known. When measurements regarding particle locations are available
but sparse, direct evaluation of the forcing is intractable. Nevertheless, the
forcing for finite-size particles can be determined using adjoint-based data
assimilation. This inverse problem is formulated with the framework of
optimization, where the cost function is defined as the difference between the
measured and predicted particle locations. The gradient of the cost function,
with respect to the forcing can be calculated from the adjoint dynamics. When
measurements are subject to Gaussian noise, samples within the probability
distribution of the forcing can be drawn using Hamiltonian Monte Carlo. The
algorithm is tested in the Arnold-Beltrami-Childress flow as well as the
homogeneous isotropic turbulence. Results demonstrate that the forcing can only
be determined accurately for particle Reynolds number between 1 and 5, where
the majority of Reynolds number history along the particle trajectory falls in
Solving optimal control problems governed by random Navier-Stokes equations using low-rank methods
Many problems in computational science and engineering are simultaneously
characterized by the following challenging issues: uncertainty, nonlinearity,
nonstationarity and high dimensionality. Existing numerical techniques for such
models would typically require considerable computational and storage
resources. This is the case, for instance, for an optimization problem governed
by time-dependent Navier-Stokes equations with uncertain inputs. In particular,
the stochastic Galerkin finite element method often leads to a prohibitively
high dimensional saddle-point system with tensor product structure. In this
paper, we approximate the solution by the low-rank Tensor Train decomposition,
and present a numerically efficient algorithm to solve the optimality equations
directly in the low-rank representation. We show that the solution of the
vorticity minimization problem with a distributed control admits a
representation with ranks that depend modestly on model and discretization
parameters even for high Reynolds numbers. For lower Reynolds numbers this is
also the case for a boundary control. This opens the way for a reduced-order
modeling of the stochastic optimal flow control with a moderate cost at all
stages.Comment: 29 page
Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics
The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end
Technical Evaluation Report for Symposium AVT-147: Computational Uncertainty in Military Vehicle Design
The complexity of modern military systems, as well as the cost and difficulty associated with experimentally verifying system and subsystem design makes the use of high-fidelity based simulation a future alternative for design and development. The predictive ability of such simulations such as computational fluid dynamics (CFD) and computational structural mechanics (CSM) have matured significantly. However, for numerical simulations to be used with confidence in design and development, quantitative measures of uncertainty must be available. The AVT 147 Symposium has been established to compile state-of-the art methods of assessing computational uncertainty, to identify future research and development needs associated with these methods, and to present examples of how these needs are being addressed and how the methods are being applied. Papers were solicited that address uncertainty estimation associated with high fidelity, physics-based simulations. The solicitation included papers that identify sources of error and uncertainty in numerical simulation from either the industry perspective or from the disciplinary or cross-disciplinary research perspective. Examples of the industry perspective were to include how computational uncertainty methods are used to reduce system risk in various stages of design or development
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