Coupling Schemes for Multiphysics Reactor Simulation

Mahadeven, Vijay; Ragusa, Jean C.

doi:10.2172/920420

Cited by 2 publications

(2 citation statements)

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“…The local truncation error term is same as Eq. (5-20): (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25) and the modified equation is…”

Section: Time Step Sensitivity Convergence Study and Resultsmentioning

confidence: 99%

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Extended Forward Sensitivity Analysis for Uncertainty Quantification

Zhao¹,

Mousseau²

2008

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This report presents the forward sensitivity analysis method as a means for quantification of uncertainty in system analysis. The traditional approach to uncertainty quantification is based on a "black box" approach. The simulation tool is treated as an unknown signal generator, a distribution of inputs according to assumed probability density functions is sent in and the distribution of the outputs is measured and correlated back to the original input distribution. This approach requires large number of simulation runs and therefore has high computational cost. Contrary to the "black box" method, a more efficient sensitivity approach can take advantage of intimate knowledge of the simulation code. In this approach equations for the propagation of uncertainty are constructed and the sensitivity is solved for as variables in the same simulation. This "glass box" method can generate similar sensitivity information as the above "black box" approach with couples of runs to cover a large uncertainty region. Because only small numbers of runs are required, those runs can be done with a high accuracy in space and time ensuring that the uncertainty of the physical model is being measured and not simply the numerical error caused by the coarse discretization.In the forward sensitivity method, the model is differentiated with respect to each parameter to yield an additional system of the same size as the original one, the result of which is the solution sensitivity. The sensitivity of any output variable can then be directly obtained from these sensitivities by applying the chain rule of differentiation. We extend the forward sensitivity method to include time and spatial steps as special parameters so that the numerical errors can be quantified against other physical parameters. This extension makes the forward sensitivity method a much more powerful tool to help uncertainty analysis. By knowing the relative sensitivity of time and space steps with other interested physical parameters, the simulation can be run at appropriate time and space steps that ensure numerical sensitivities will not affect the confidence of the physical parameter sensitivity results.

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“…The local truncation error term is same as Eq. (5-20): (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25) and the modified equation is…”

Section: Time Step Sensitivity Convergence Study and Resultsmentioning

confidence: 99%

“…We will first use the thermal wave problem [15,16] as an example to investigate the forward sensitivity method. This problem has very useful analytical solutions for the problem itself and all the parameter sensitivities so that the numerical algorithms can be accurately verified.…”

Section: Physical Modelmentioning

confidence: 99%