Abstract
Keywords:
Meshfree Methods, Finite Pointset Method, General Finite Difference, Moving Least Squares, Upwind Techniques, Airbag Deployment Simulations, PAM-CRASH
Abstract:
In the past years, the so-called Finite Pointset Method (FPM), a new meshfree numerical method for solving problems in gas- and hydrodynamics, has been developed at ITWM in Kaiserslautern. The main ideas of FPM are as follows. - Fluid flows, governed by the compressible Euler equations, are modeled. - The flow domain is filled with a cloud of numerical points (also called particles). Particles are carriers of all information relevant to the considered physical problem. - There is no meshing of the particles. Instead, particles in a ball around some point are called neighbors. The radius of the ball (smoothing length) is user given or adaptive, and may change locally. - Derivatives, used to approximate the Euler equations, are modeled by the moving least squares (MLS) operator. - The scheme is based on a Lagrange idea, i.e. the particles are moving with fluid velocity. Therefore, an excellent adaptivity to dynamic geometries or free surfaces is given. - It will be shown that the scheme is locally and continuously conservative. - An upwind idea is presented which is essential to stabilize the scheme. By its character, FPM is a general finite difference approach. FPM was successfully employed already in several industrial projects. Special effort was done in the field of airbag deployment simulations in case of car accidents. Here, FPM was integrated into the commercial PAM-CRASH software, developed by ESI-Group.