From a nonaqueous alkali-metal salt solution, it is possible to observe sonoluminescence (SL) at low acoustic drive levels with the ratio of the acoustic pressure amplitude to the ambient pressure being about 1. In this case, the emission has a narrowband spectral content and consists of a few flashes of light from a levitated gas bubble going through an unstable motion. A systematic statistica...

This work develops fast and adaptive algorithms for numerically solving nonlinear partial di erential equations of the form ut = Lu +N f(u) where L and N are linear di erential operators and f(u) is a nonlinear function. These equations are adaptively solved by projecting the solution u and the operators L and N into a wavelet basis. Vanishing moments of the basis functions permit a sparse repr...

In this article, we report on the development of hybrid numerical models used to simulate free surface, i.e., wave, hydrodynamics, wave-structure interactions, wave breaking and nearshore transformation, and wave-induced sediment transport. Specifically, a two(2D) or three-dimensional (3D) numerical wave tank (NWT), based on Fully Nonlinear Potential Flow (FNPF) equations, is used to simulate f...

this work concerns the peristaltic flow of a williamson fluid model in an inclined asymmetric channel under combined effects of heat and mass transfer. the governing nonlinear partial differential equations are simplified under the lubrication approach and then solved analytically and numerically. the analytical results are computed with the help of regular perturbation and the numerical result...

A node-based smoothed finite element method (NS-FEM-T3) using triangular elements and a n-sided polygonal edge-based smoothed FEM (nES-FEM) using polygonal elements is combined to give the smoothed coupled NS/nES-FEM for dynamic analysis of twodimensional (2D) fluid–solid interaction problems based on the pressure–displacement formulation. In the present method, the NS-FEM-T3 is used for the fl...

requires the development of new algorithms, which are introduced in this paper. This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form ut 5 Any wavelet-expansion approach to solving differential Lu 1 N f (u), where L and N are linear differential operators and equations is essentially a projection method. In a projection f (u...

in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...

A brief description of effective Navier-Stokes (NS) numerical technique for high temperature gas flows simulation (HIGHTEMP) is given. The NS codes have been developed for various gas-phase models from perfect gas to thermally and chemically nonequilibrium multicomponent and multitemperature gas medium. Slip effects, finite rate energy exchanges, surface catalysis and ablation can be taken into...

We study a recent regularization of the Navier-Stokes equations, the NS-ω model. This model has similarities to the NS-α model, but its structure is more amenable to be used as a basis for numerical simulations of turbulent flows. In this report we present the model and prove existence and uniqueness of strong solutions as well as convergence (modulo a subsequence) to a weak solution of the Nav...

In this article, we present an error estimate of the derivative approximation by the local multiquadricbased differential quadrature (LMQDQ) method. Radial basis function is different from the polynomial approximation, in which Taylor series expansion is not applicable. So, the present analysis is performed through the numerical solution of Poisson equation. It is known that the approximation e...