A short review of wavelet-based adaptive methods for modeling and simulation incompressible turbulent flows is presented. Wavelet-based computational approaches different fidelities are recast into an integrated hierarchical eddy-capturing turbulence framework. The wavelet threshold filtering procedure the associated wavelet-filtered Navier–Stokes equations briefly discussed, along with colloca...

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

This paper introduces the hybrid wavelet collocation–Brinkman penalization method for solving the Navier–Stokes equations in arbitrarily complex geometries. The main advantages of the wavelet collocation method and penalization techniques are described, and a brief summary of their implementation is given. The hybrid method is then applied to a simple ow around cylinders with both periodic and ...

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

The paper presents an uncertainty propagation method for problems with discontinuous surface responses. Based on Pade-Legendre (PL) approximants in multiple dimensions, the proposed method is global and non-intrusive. In this work, the PL method is applied to a model problem of supersonic flows with multiple possible flow configurations, depending on the uncertain input parameters. The results ...