Abstract
Random processes play a significant role in stochastic analysis of mechanical systems, structures, fluid mechanics, and other engineering systems. In this paper, a numerical method for series representation of random processes, with specified mean and correlation functions, in wavelet bases is presented. In this method, the Karhunen-Loeve expansion approach is used to represent a process as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets. The eigenfunctions satisfy an integral eigenvalue problem. Using the above approximations, the integral eigenvalue problem is converted to a matrix (finite dimensional) eigenvalue problem. Numerical algorithms are discussed to compute one- and two-dimensional wavelet transforms of certain functions, and the resulting equations are solved to obtain the eigenvalues and the eigenfunctions. The scheme provides an improvement over other existing schemes. Two examples are considered to show the feasibility and effectiveness of this method. Numerical studies show that the results obtained using this method compare well with analytical techniques.
Coherent vorticity and current density simulation of three-dimensional magnetohydrodynamic turbulence using orthogonal wavelets
