Multiscale Approximation of Vortex Patches
نویسندگان
چکیده
We propose an adaptive scheme, based on multiscale decomposition into interpolatory wavelet bases, to simulate the evolution of vortex patches associated to solutions of the two-dimensional Euler equations. This scheme is based on fast algorithms that relate the numerically signiicant wavelet coeecients with the irregular sampling of the boundary of the patch on an adaptive grid. This method allows to analyse the evolution of the sin-gularities on this boundary at a low computational cost.
منابع مشابه
Far-field perturbations of vortex patches.
In this paper I investigate the dynamics of vortex patches in the Yudovitch phase space. I derive an approximation for the evolution of the vorticity in the case of nested vortex patches with distant boundaries, and study its long-time behaviour.
متن کاملGeometric phases for corotating elliptical vortex patches
We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek @J. Fluid Mech. 167, 95–115 ~1986!# we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian...
متن کاملMultiscale Union Regions Adaptive Sparse Representation for Hyperspectral Image Classification
Sparse Representation has been widely applied to classification of hyperspectral images (HSIs). Besides spectral information, the spatial context in HSIs also plays an important role in the classification. The recently published Multiscale Adaptive Sparse Representation (MASR) classifier has shown good performance in exploiting spatial information for HSI classification. But the spatial informa...
متن کاملConvergence of a Galerkin Method for 2-D Discontinuous Euler Flows
We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity: ω0 ∈ L2(Ω). Furthermore, when ω0 ∈ L∞(Ω), the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex pa...
متن کاملElliptic vortex patches: coasts and chaos
We investigate the interaction of ocean vortex patches with boundaries via the elliptic moment model of Melander, Zabusky & Stysek [13], under which vortex patches are approximated as elliptic regions of uniform vorticity. The interaction with a straight boundary is shown to reduce to the problem of an ellipse in constant strain, as previously investigated by Kida [9]. Interactions with more co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 60 شماره
صفحات -
تاریخ انتشار 2000