Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented ...

Loosely speaking, let us explain on a simple exemple what is a meshfree method: let us pretend that we want to analyze the properties of some function whose support is included in Ω approximated by finite elements or wavelets. Either we construct some ad hoc wavelets or splines whose support is included in Ω, or we use the whole family of splines or wavelets defined on IR. The latest method is ...

We present the application of a meshfree method for simulations of interaction between fluids and flexible structures. As a flexible structure we consider a sheet of paper. In a two-dimensional framework this sheet can be modeled as curve by the dynamical Kirchhoff-Love theory. The external forces taken into account are gravitation and the pressure difference between upper and lower surface of ...

Since meshfree particle methods have advantages on simulating the problems involving extremely large deformations, fractures etc., they become attractive options to be used in the hierarchical multiscale modeling to approximate a large number of atoms. We propose a nanoscale meshfree particle method with the implementation of the quasicontinuum technique in this paper. The intrinsic properties ...

This paper presents a convex meshfree framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems. The generalized meshfree approximation (GMF) method using inverse tangent basis functions and cubic spline weight functions is employed to construct the first-order convex approximation which exhibits a weak Kronecker-delta property at the waveguide bo...

Keywords: Meshless method Coupled radiative–conductive transfer Discrete ordinates Even parity Complex geometries a b s t r a c t A meshless method DAM is employed to solve the coupled radiative and conductive heat transfer problem in a semi-transparent medium enclosed in complex 2D and 3D geome-tries. The meshless method for radiative transfer is based on the even parity formulation of the dis...

The diffuse element method developed by Nayroles et al. is a new way for solving partial differential equations. In this method, only a mesh of nodes and a boundary description is needed to develop the Galerkin equations. The approximating functions are polynomials fitted to the nodal values of each local domain by a weighted least squares approximation. Belytschko et al. developed an alternati...

Meshfree methods are the topic of recent research in many areas of computational science and approximation theory. These methods come in various flavors, most of which can be explained either by what is known in the literature as radial basis functions (RBFs), or in terms of the moving least squares (MLS) method. Over the past several years meshfree approximation methods have found their way in...