Abstract

A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.

Abstract

This paper presents tests and applications related to the Method of the Fundamental Solutions (MFS) for nonhomogeneous diffusion equations. The dual reciprocity method was applied to approximate the particular solution and different MSF were applied to solve the homogeneous equation. The computational accuracy for three different versions submitted to diverse geometries, initial, boundary and nonhomogeneous conditions is compared. The first version is the MFS, based on the fundamental solutions to the modified Helmholtz operator; the second and third versions are based on transient fundamental solutions proposed directly for the diffusion governing equation. This paper evaluates particularities for all methods proposed as the solution advances in time until steady-state solutions are reached. The developed computer codes are applied to several examples with the intention of demonstrating the methods’ effectiveness and applicability.

Abstract

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented.