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An adaptive numerical method for solving partial differential equations is developed. The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O(N) hierarchical finite difference scheme, which takes advantage of wavelet mul-tilevel decomposition, is used for(More)
Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed(More)
A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular(More)
A class of lters for large eddy simulations of turbulent inhomogeneous ows is presented. A general set of rules for constructing discrete lters in complex geometry is given and examples of such lters are presented. With these lters the commutation error between numerical diierentiation and ltering can be made arbitrarily small, allowing for derivation of a(More)
Liandrat and Tchiamichian [2], Bacry et al. [3], Maday and Ravel [4], and Bertoluzza et al. [5] have shown that A dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations. The the multiresolution structure of wavelet bases is a simple multilevel structure of the algorithm provides a simple(More)
Large-eddy simulation ͑LES͒ with regular explicit filtering is investigated. The filtered-scale stress due to the explicit filtering is here partially reconstructed using the tensor-diffusivity model: It provides for backscatter along the stretching direction͑s͒, and for global dissipation, both also attributes of the exact filtered-scale stress. The(More)
In this work coherent vortex simulation (CVS) and stochastic coherent adaptive large eddy simulation (SCALES) simulations of decaying incompressible isotropic turbulence are compared to DNS and large eddy simulation (LES) results. Current LES relies on, at best, a zonally adapted filter width to reduce the computational cost of simulating complex turbulent(More)
Adaptive wavelet-collocation numerical methods (AWCM) for solving the Euler equations for compressible flow with shock discontinuities are described. An algorithm is constructed to add a minimal but sufficient amount of viscosity in the vicinity of steep gradients, based on the behavior of wavelet coefficients there. This selective addition of numerical(More)
Two mathematical approaches are combined to calculate high Reynolds number in-compressible fluid-structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid boundaries of arbitrary complexity. We also implement a wavelet-based multilevel solver for(More)
A fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed. The computational cost of the algorithm is independent of the dimensionality of the problem and is O(N), where N is the total number of collocation points. The method can handle general boundary conditions. The multilevel(More)