Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation

Lu, Shang-Yi; Sagaut, Pierre

doi:10.1002/fld.1386

Cited by 21 publications

(11 citation statements)

References 17 publications

(30 reference statements)

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“…+ ) of (1) (resp. (3) ) allows the Rankine-Hugoniot conditions to be written, for the first two components of (1a), as…”

Section: Fluxes Calculationmentioning

confidence: 99%

“…Typically, the classical empirical (or finite difference) approach consists in performing two simulations with two slightly different values of the parameter of interest and computing the difference between both results, normalized by the parameter variation. An example of another efficient approach, known as complex differentiation, can be found in [3]. These methods are best-suited to the analysis of complex models dealing with complex geometries, or to the analysis of model response, where the transfer function between 982 C. DELENNE ET AL.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flows

Delenne

Finaud-Guyot

Guinot

et al. 2010

Numerical Methods in Fluids

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SUMMARYA finite volume-based numerical technique is presented concerning the sensitivity of the solution of the one-dimensional Shallow Water Equations with scalar transport. An approximate Riemann solver is proposed for direct sensitivity calculation even in the presence of discontinuous solutions. The Shallow Water Sensitivity Equations are first derived as well as the expressions of the sensitivity source terms, initial and boundary conditions. The numerical technique is then detailed and application examples are provided to assess the method's efficiency in estimating the sensitivity to different parameters (friction coefficient and initial and boundary conditions). The application of the dam-break problem to a trapezoidal channel is also provided. The comparison with the analytical solution and the classical empirical approach illustrates the usefulness of the direct sensitivity calculation.

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“…+ ) of (1) (resp. (3) ) allows the Rankine-Hugoniot conditions to be written, for the first two components of (1a), as…”

Section: Fluxes Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flows

Delenne

Finaud-Guyot

Guinot

et al. 2010

Numerical Methods in Fluids

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“…However, it does not offer a saving of resources when compared to using finite-differences since the problem must be solved at a perturbed state for each parameter (see e.g. [24][25][26].) (3) Sensitivity equation method (SEM): The SEMs numerically solve a set of PDEs for the sensitivities.…”

Section: Formulation For the Direct Numerical Simulationmentioning

confidence: 99%

Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

Hay

Borggaard

Akhtar

et al. 2010

Journal of Computational Physics

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Reduced-order models for parameter dependent geometries based on shape sensitivity analysis Hay, A.; Borggaard, J.; Akhtar, I.; Pelletier, D.Contact us / Contactez nous: nparc.cisti@nrc-cnrc.gc.ca. The proper orthogonal decomposition (POD) is widely used to derive low-dimensional models of large and complex systems. One of the main drawback of this method, however, is that it is based on reference data. When they are obtained for one single set of parameter values, the resulting model can reproduce the reference dynamics very accurately but generally lack of robustness away from the reference state. It is therefore crucial to enlarge the validity range of these models beyond the parameter values for which they were derived. This paper presents two strategies based on shape sensitivity analysis to partially address this limitation of the POD for parameters that define the geometry of the problem at hand (design or shape parameters.) We first detail the methodology to compute both the POD modes and their Lagrangian sensitivities with respect to shape parameters. From them, we derive improved reduced-order bases to approximate a class of solutions over a range of parameter values. Secondly, we demonstrate the efficiency and limitations of these approaches on two typical flow problems: (1) the one-dimensional Burgers' equation; (2) the two-dimensional flows past a square cylinder over a range of incidence angles.

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“…In other words, it measures the importance of changes in the flow response to perturbations of the model parameters. There are several means of computing sensitivities [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Finite element and sensitivity analysis of thermally induced flow instabilities

Giguère

Ilinca

Pelletier

2010

Numerical Methods in Fluids

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This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.

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Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation

Cited by 21 publications

References 17 publications

Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flows

Sensitivity of the 1D shallow water equations with source terms: Solution method for discontinuous flows

Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

Finite element and sensitivity analysis of thermally induced flow instabilities

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