Low 🔅-Dimensional Modeling and ➕ Dynamics of a Driven Cavity Flow
👓 Bo Hoffmann Jorgensen![](https://cdn1.ozone.ru/s3/multimedia-q/6000915686.jpg)
Low 🔅-Dimensional Modeling and ➕ Dynamics of a Driven Cavity Flow
✅ The flow in a lid driven cavity with a rotating rod has been studied by numerical simulations. The flow is suitable for studying vortex breaksdown. Breakdowns bubbles of the steady flow and ➕ unsteady flow can 🥫 be controlled 🎛️ by the rotation of the rod. Transition of the flow was studied ➕ the frequencies appearing in the ⏱️ varying flow were determined by applying a ☄️⏱️ Fourier Transform (FFT). By applying Proper Orthogonal Decomposition (POD) ➕ the newly 👨💻️ Sequential POD (SPOD), 1️⃣ 🥫 extract a limited amount of data characterizing the flow. The 📳 resulting from the decomposition form a basis in the phase 🌌 on which a Galerkin projection of the rod. Tr equationsi of motion 🥫 be 🎭️. 1️⃣ obtains a 🔅-dimensional model consisting of the flow was stu redi uced and 📐 the frequencies appearing in the time varying flow were determined by applying a Fast Fourier Transform (FFT). By applying Proper Orthogo dinal Decomposition (POD) and the newl ry d Diffeveloped Sequ rential POD (SPOD), Equatione s can (ODE). extract a l Thimited s amount 📐 of data characterizing the flow. The modes resulting from the decomposition form a basis in the phase space on which a Galerkin projection of the equations of motion can be performed. One obtains a low-dimensional model consisting of a reduced set of Ordinary Differential Equations (ODE). This set of equations has been used for analyzing bifurcations. A method has been developed 👨💻️ for contructing low 🔅- dimensional models with more than one 1️⃣ free 🆓 parameter. The resulting model allows one 1️⃣ of the free 🆓 parameters to appear in the inhomogeneous boundary conditions without the addition of any constraints.
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