Meshfree methods

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

The Meshfree Localized Petrov-Galerkin Approach in Slope Stability Analysis

Abstract: Abstract The article focuses on the use of the meshfree numerical method in the field of slope stability computations. There are many meshfree implementations of numerical methods. The article shows the results obtained using the meshfree localized Petrov-Galerkin method (MLPG) – localized weak-form of the equilibrium equations with an often used elastoplastic material model based on Mohr-Coulomb (MC) yield criterion. The most important aspect of MLPG is that the discretization process uses a set of nodes instead of elements. Node position within the computational domain is not restricted by any prescribed relationship. The shape functions are constructed using just the set of nodes present in the simple shaped domain of influence. The benchmark slope stability numerical model was performed using the developed meshfree computer code and compared with conventional finite element (FEM) and limit equilibrium (LEM) codes. The results showed the ability of the implemented theoretical preliminaries to solve the geotechnical stability problems.

The Application of the Generalized Finite Difference Method (GFDM) for Modelling Geophysical Test

Abstract: The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.

A stokeslets approach for the numerical solution of Brinkman systems

Abstract: In this work we present some properties of unsteady hydrodynamic potentials in order to justify a meshfree numerical method for Brinkman systems with Dirichlet and Neumann boundary conditions. The problems here addressed concerns interior 2D problems and can be easily extended for exterior and 3D problems. We will illustrate the feasibility of the methods with some numerical simulations.

A Multi-Phase Flow Model Incorporated with Population Balance Equation in a Meshfree Framework

Abstract: This study deals with the numerical solution of a meshfree coupled model of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) for liquid-liquid extraction columns. In modeling the coupled hydrodynamics and mass transfer in liquid extraction columns one encounters multidimensional population balance equation that could not be fully resolved numerically within a reasonable time necessary for steady state or dynamic simulations. For this reason, there is an obvious need for a new liquid extraction model that captures all the essential physical phenomena and still tractable from computational point of view. This thesis discusses a new model which focuses on discretization of the external (spatial) and internal coordinates such that the computational time is drastically reduced. For the internal coordinates, the concept of the multi-primary particle method; as a special case of the Sectional Quadrature Method of Moments (SQMOM) is used to represent the droplet internal properties. This model is capable of conserving the most important integral properties of the distribution; namely: the total number, solute and volume concentrations and reduces the computational time when compared to the classical finite difference methods, which require many grid points to conserve the desired physical quantities. On the other hand, due to the discrete nature of the dispersed phase, a meshfree Lagrangian particle method is used to discretize the spatial domain (extraction column height) using the Finite Pointset Method (FPM). This method avoids the extremely difficult convective term discretization using the classical finite volume methods, which require a lot of grid points to capture the moving fronts propagating along column height.