This contribution concerns the construction of meshless Lagrangian particle methods for the numerical simulation of multiscale phenomena in linear transport problems, where mass conservative discretization methods are essentially required. The proposed discretization scheme works with a finite set of unstructured nodes, each corresponding to one flow particle. In this method, corresponding part...

We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dial grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points xi. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that sp...

1. Research Student, Department of Mechanical Engineering, School of Engineering, Gautam Buddha University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India 2. Assistant Professor, Department of Mechanical Engineering, School of Engineering, Gautam Buddha University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India; 3. Assistant Professor, Department of Mechanical Engineering, S...

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of...

This paper advocates a method for real-time physical deformation and arbitrary cutting simulation of heterogeneous objects with multi-material distribution, whose originality centers on the tight coupling of domain-specific finite element method (FEM) 1 and material-distance-aware meshless approach in a CUDA-centric parallel simulation framework. We employ hierarchical hexahedron serving as bas...

An algorithm for use with several meshless schemes is presented based on a local extremum diminishing property. The scheme is applied to the Euler equations in two dimensions. The algorithm is suitable for use with many meshless schemes, three of which are detailed here. First, a method based on Taylor series expansion and least squares is highlighted. Next, a similar least squares method is us...

This work is a natural extension of the work done in Part II of this series. A new partition of unity | the synchronized reproducing kernel (SRK) interpolant|is proposed within the framework of moving least square reproducing kernel representation. It is a further development and generalization of the reproducing kernel particle method (RKPM), which demonstrates some superior computational capa...

in this paper, an adaptive meshless method of line is applied to distribute the nodes in the spatial domain. in many cases in meshless methods, it is also necessary for the chosen nodes to have certain smoothness properties. the set of nodes is also required to satisfy certain constraints. in this paper, one of these constraints is investigated. the aim of this manuscript is the implementation ...