Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Meshfree methods for computational fluid dynamics

Abstract: The paper deals with the convergence problem of the SPH (Smoothed Particle Hydrodynamics) meshfree method for the solution of fluid dynamics tasks. In the introductory part, fundamental aspects of mesh- free methods, their definition, computational approaches and classification are discussed. In the following part, the methods of local integral representation, where SPH belongs are analyzed and specifically the method RKPM (Reproducing Kernel Particle Method) is described. In the contribution, also the influence of boundary conditions on the SPH approximation consistence is analyzed, which has a direct impact on the convergence of the method. A classical boundary condition in the form of virtual particles does not ensure a sufficient order of consistence near the boundary of the definition domain of the task. This problem is solved by using ghost particles as a boundary condition, which was implemented into the SPH code as part of this work. Further, several numerical aspects linked with the SPH method are described. In the concluding part, results are presented of the application of the SPH method with ghost particles to the 2D shock tube example. Also results of tests of several parameters and modifications of the SPH code are shown.

A least squares based meshfree technique for the numerical solution of the flow of viscoelastic fluids: A node enrichment strategy

Abstract: A fully implicit least-squares-based meshfree method is used to solve the governing equations of viscoelastic fluid flow. Here, pressure is connected to the continuity equation by an artificial compressibility technique. A radial point interpolation method is used to construct the meshfree shape functions. The method is used to solve two benchmark problems. Thanks to the flexibility of meshfree methods in domain discretization, a simple node enrichment strategy is used to discrete the problem domain more purposefully. It is shown that the introduced enrichment process have a positive effect on the accuracy of the results.

Meshless Vector Radial Basis Functions With Weak Forms

Abstract: Meshless methods construct their shape functions based on scattered nodes in the domain. One drawback of this approach is the presence of nonphysical modes in the numerical solution when dealing with vector problems due to the lack of the divergence free condition, in a similar way that occurs with the node-based finite-element method. On the other hand, vector radial basis functions were developed to produce numerical approximations that satisfy the divergence free condition. This paper presents the usage of those functions in conjunction with weak forms to solve vector electromagnetic problems. Numerical tests involving the Maxwell eigenvalue problem and the wave propagation in a waveguide are solved to demonstrate that the numerical solution is not corrupted with spurious modes.

Numerical simulation of soil-water jet interaction with smoothed particle hydrodynamics

Abstract: Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian particle method, which has been applied to different areas in sciences and industrial applications. In this work, SPH is used to simulate the soil-water jet interaction and erosion. In the simulation, water is modelled as a viscous fluid with weak compressibility and the soil is assumed to be an elastic-perfectly plastic material. The stress states of soil in the plastic flow regime follow the Drucker-Prager failure criterion. Both the shear and tensile criterions are used for the yield of soil particles if the yield point is reached and the total stress of the particle is scaled. Instead of computing particle pressure from an equation of state, the spherical stress is computed by dividing total stress into spherical stress and deviatoric stress. The interaction of coupling interfaces is strengthened by a penalty function to avoid unphysical penetration between particles from different materials. The obtained numerical results have shown that SPH could be a valuable method for the simulation of complex soil water interaction.

Meshfree point interpolation methods for analysis of piezoelectric structures

Abstract: This paper summarizes the studies on meshfree point interpolation method (PIM) for static and dynamic analysis of piezoelectric structures. In the PIM methods, the problem domain is represented by a set of properly scattered nodes. The displacements and the electric potential of a point are interpolated by the values of nodes in its local support domain using shape functions derived from point interpolation scheme. Galerkin formulation is used to establish a set of system equations for arbitrary-shaped piezoelectric structures. Numerical examples are presented to demonstrate the validity and convergence of the present method and their results compare well with the conventional FEM results from ABAQUS as well as the experimental ones.