69 research outputs found
Proper orthogonal decomposition closure models for fluid flows: Burgers equation
This paper puts forth several closure models for the proper orthogonal
decomposition (POD) reduced order modeling of fluid flows. These new closure
models, together with other standard closure models, are investigated in the
numerical simulation of the Burgers equation. This simplified setting
represents just the first step in the investigation of the new closure models.
It allows a thorough assessment of the performance of the new models, including
a parameter sensitivity study. Two challenging test problems displaying moving
shock waves are chosen in the numerical investigation. The closure models and a
standard Galerkin POD reduced order model are benchmarked against the fine
resolution numerical simulation. Both numerical accuracy and computational
efficiency are used to assess the performance of the models
A Two-Level Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean
In this paper we proposed a two-level finite element discretization of the
nonlinear stationary quasi-geostrophic equations, which model the wind driven
large scale ocean circulation. Optimal error estimates for the two-level finite
element discretization were derived. Numerical experiments for the two-level
algorithm with the Argyris finite element were also carried out. The numerical
results verified the theoretical error estimates and showed that, for the
appropriate scaling between the coarse and fine mesh sizes, the two-level
algorithm significantly decreases the computational time of the standard
one-level algorithm.Comment: Computers and Mathematics with Applications 66 201
- …