The mesh may be recreated during simulation (a process called remeshing), but this can also introduce error, since all the existing data points must be mapped onto a new and different set of data points. If the mesh becomes tangled or degenerate during simulation, the operators defined on it may no longer give correct values. These operators are then used to construct the equations to simulate-such as the Euler equations or the Navier–Stokes equations.īut in simulations where the material being simulated can move around (as in computational fluid dynamics) or where large deformations of the material can occur (as in simulations of plastic materials), the connectivity of the mesh can be difficult to maintain without introducing error into the simulation. In such a mesh, each point has a fixed number of predefined neighbors, and this connectivity between neighbors can be used to define mathematical operators like the derivative. Compared to the experimental results for polyurethane foaming process in a conical beaker, the numerical results using the FPM code are acceptable.Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes of data points. The expansion of the mixture is governed by the front velocity which is calculated by solving the Navier-Stokes equations. This coupling is displayed through the dependency of the fluid viscosity to the evolution of the temperature and the chemical reactions present during the foaming process. To do so, we have adopted a theoretical model describing the contribution of the chemical kinetics and the rheological coupling characterizing such process. The efficiency of this method is pointed by studying the problem of polyurethane foaming. It consists in representing the fluid domain by a set of particles. This method called Finite Point Method (FPM) has been developed by Kuhnert. In this work, a meshfree Lagrangian method is used to avoid these problems. Abstract: For the numerical simulation of fluid mechanics problems in complex geometries, the use of the classical grid methods such as the finite element method and the finite volume method can give rise to several problems related to the deformation of the mesh.

Challenges in meshfree methods