At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.
Abstract. The Finite Point Method (FPM) is a meshless technique which is based on both, aWeighted 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 threedimensional 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.
Purpose -The purpose of this paper is to describe a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural solver for unsteady simulations of ram-air type parachutes. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique. Design/methodology/approach -For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly nonlinear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness. Findings -A simple and effective numerical tool for the analysis of parachutes has been developed. Originality/value -An analysis code has been developed which addresses the needs of ram-air parachute designers. The software delivers reasonably accurate results in a short time using modest hardware. It can therefore assist the design process, which nowadays relies on empirical methods. IntroductionThe numerical simulation of parachutes is a challenging coupled problem. From the structural point of view, parachutes are complex in design and behaviour. Braced membranes, such as parachute canopies, cannot equilibrate an arbitrary set of loads unless drastic geometrical changes take place; thus, the structural response is extremely nonlinear. The lack of bending stiffness of the structural components makes them buckle (wrinkle) under compressive loads, exhibiting an asymmetric behaviour. Moreover, the interaction and contact between the different structural elements often has to be accounted for in order to properly model the problem. The flow surrounding the parachute is also complex and highly unsteady in some flight stages of the parachutes (e.g. deployment and inflation). The aerodynamic model adopted should also account for massive flow separation, the presence of large unsteady wakes and aerodynamic interactions between the structural components. The nature of the applied forces, which depend heavily on the structural response of the parachute, adds an extra layer of complexity to the analysis. As the magnitude and direction of the aerodynamic forces (mainly follower pressure loads) are not known in advance but
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