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A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. (arXiv:1709.06422v2 [math.NA] UPDATED)
来源于:arXiv
Partial differential equations (PDE) often involve parameters, such as
viscosity or density. An analysis of the PDE may involve considering a large
range of parameter values, as occurs in uncertainty quantification, control and
optimization, inference, and several statistical techniques. The solution for
even a single case may be quite expensive; whereas parallel computing may be
applied, this reduces the total elapsed time but not the total computational
effort. In the case of flows governed by the Navier-Stokes equations, a method
has been devised for computing an ensemble of solutions. Recently, a
reduced-order model derived from a proper orthogonal decomposition (POD)
approach was incorporated into a first-order accurate in time version of the
ensemble algorithm. In this work, we expand on that work by incorporating the
POD reduced order model into a second-order accurate ensemble algorithm.
Stability and convergence results for this method are updated to account for
the POD/ROM ap 查看全文>>