Using sensitivity equations for chemically reacting flows

Godfrey, Andrew G.; Eppard, William M.; Cliff, Eugene M.

doi:10.2514/6.1998-4805

Cited by 12 publications

(6 citation statements)

References 5 publications

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“…[8]). Monte Carlo methods are often referred to as "embarrassingly parallel" because of their efficiency in parallelization.…”

Section: Coupling Osdes With Rqmcmentioning

confidence: 93%

“…For this problem, since the analytical evaluation of the first moment E[u] is not available, we resort to one-dimensional Gauss-Hermite quadrature to approximate it with high accuracy. Specifically, the number of quadrature points is taken as 2 8 , in order to guarantee that the numerical value has higher precision than the estimates of the most accurate estimator in our simulations. We call this quadrature approximation the "numerically exact solution".…”

Section: Generalized Burgers Equation With Stochastic Viscositymentioning

confidence: 99%

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Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives

Liu

Hussaini

Ökten

2013

Applied Numerical Mathematics

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“…[8]). Monte Carlo methods are often referred to as "embarrassingly parallel" because of their efficiency in parallelization.…”

Section: Coupling Osdes With Rqmcmentioning

confidence: 93%

Section: Generalized Burgers Equation With Stochastic Viscositymentioning

confidence: 99%

Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives

Liu

Hussaini

Ökten

2013

Applied Numerical Mathematics

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“…• identification of key parameters controlling the flow (Blackwell et al 1998) (the important parameters), • identification of parameters that have little effect (Blackwell et al 1998) (the negligible parameters), • fast evaluation of solution for nearby values of the parameters (Godfrey et al 1998),…”

Section: Introductionmentioning

confidence: 99%

Application of a sensitivity equation method to the k–ε model of turbulence

et al. 2007

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In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k-model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.

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“…As such, sensitivity analysis can be used to generate the gradients necessary for optimization algorithms [1][2][3]. In addition, local gradient information from the sensitivity analysis can be used to approximate flow fields 'near' the given baseline case [24,25]. Sensitivity analysis may be performed using several different numerical techniques, including finite difference, complex-step differentiation, software differentiation, and continuous sensitivity equation method.…”

Section: Sensitivity Analysis Methodsmentioning

confidence: 99%

Sensitivity analysis of low Reynolds number channel flow using the finite volume method

Kirkman

Metzger

2007

Numerical Methods in Fluids

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SUMMARYAn unsteady finite volume-based fractional step algorithm solved on a staggered grid has been developed for computing design sensitivity parameters in two-dimensional flows. Verification of the numerical code is performed for the case of low Reynolds number, pressure-driven flow through a straight channel, which has an exact steady-state solution to the Navier-Stokes equations. Sensitivity of the flow to the channel height, fluid viscosity, and imposed pressure gradient is considered. Three different numerical techniques for computing the design sensitivity parameters: finite difference, complex-step differentiation, and sensitivity equation method (SEM), are compared in terms of numerical error (relative to the exact solution), computational expense, and ease of implementation. Results indicate that, of all the three methods, complex step is the most accurate and requires the least computational time. In addition, treatment of the boundary conditions in SEM is addressed, within the framework of the present finite volume approach, with special attention given to parameter dependence in the boundary conditions. Error estimation based on the Grid Convergence Index provides a good indication of the exact error in the SEM solutions. An example of application of the use of sensitivity parameters to estimate the propagation of input uncertainty through the numerical simulation is also provided.

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Using sensitivity equations for chemically reacting flows

Cited by 12 publications

References 5 publications

Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives

Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives

Application of a sensitivity equation method to the k–ε model of turbulence

Sensitivity analysis of low Reynolds number channel flow using the finite volume method

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