9,756 research outputs found
Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.Région Poitou-Charente
An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations
In this paper, we propose an augmented subspace based adaptive proper
orthogonal decomposition (POD) method for solving the time dependent partial
differential equations. By augmenting the POD subspace with some auxiliary
modes, we obtain an augmented subspace. We use the difference between the
approximation obtained in this augmented subspace and that obtained in the
original POD subspace to construct an error indicator, by which we obtain a
general framework for augmented subspace based adaptive POD method. We then
provide two strategies to obtain some specific augmented subspaces, the random
vector based augmented subspace and the coarse-grid approximations based
augmented subspace. We apply our new method to two typical 3D
advection-diffusion equations with the advection being the Kolmogorov flow and
the ABC flow. Numerical results show that our method is more efficient than the
existing adaptive POD methods, especially for the advection dominated models.Comment: 28 pages, 4 figures, 7 table
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