Predictability and uncertainty in CFD. (English) Zbl 1032.76662
Summary: CFD has reached some degree of maturity today, but the new question is how to construct simulation error bars that reflect uncertainties of the physical problem, in addition to the usual numerical inaccuracies. We present a fast Polynomial Chaos algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by Wiener-Hermite functionals, and the governing equations are formulated by employing Galerkin projections. The resulted system is deterministic, and therefore existing solvers can be used in this new context of stochastic simulations. The algorithm is applied to a second-order oscillator and to a flow-structure interaction problems. Open issues and extensions to general random distributions are presented.
MSC:
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
computational fluid dynamics; polynomial chaos; Wiener-Hermite functionals; incompressible flowsReferences:
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