TY - JOUR
T1 - A Higher-Order Ensemble/Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations
AU - Gunzburger , Max
AU - Jiang , Nan
AU - Schneier , Michael
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 608
EP - 627
PY - 2018
DA - 2018/04
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12534.html
KW - Navier-Stokes equations, ensemble computation, proper orthogonal decomposition, finite element methods.
AB - <p style="text-align: justify;">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 approach. Numerical experiments
illustrate the accuracy and efficiency of the new approach.</p>