Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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01 Jan 2007
TL;DR: In recent years, a number of meshless methods have been developed based on the finite element methods, which effectively overcoming the mesh entanglement in solving the excessive large deformation problems.
Abstract: The analysis of rubber materials is a challenging task in computational mechanics due to extremely large deformation and the nearly incompressible property of rubber. Despite the finite element methods (FEM) dealing with nonlinear structures have been well developed and a significant amount of work has been accomplished. But the widely used finite element methods are still ineffective in handling extreme material distortions due to the regularity requirement of interpolation functions and meshes. In recent years, a number of meshless methods have been developed based on the finite element methods, which effectively overcoming the mesh entanglement in solving the excessive large deformation problems. In meshless methods, the domains of interest are discretized by a scattered set of points. The successes of meshless methods are due to the development of new shape functions that allow the interpolation of field variables to be accomplished at a global level or a local level and therefore avoid the use of a mesh. These methods are ideal for modeling refinement, adaptivity, fracture problems, and large deformation problems, etc.
1 citations
TL;DR: In this article, the benefits of the Langrangian mesh-free methods were discussed and the Smoothed Particle Hydrodynamics method was proposed as an efficient method for a rapid prediction of the global mean flow in stirred reactors.
Abstract: Crystallization phenomena in stirred reactors are influenced by local hydrodynamic conditions and these must be taken into account for successful process scale-up and optimization. In this work, the available state of the art grid-based CFD methods and advantages and disadvantages of their application to mathematical modelling of batch crystallization processes were analyzed. The benefits of the Langrangian meshfree methods were discussed and the Smoothed Particle Hydrodynamics method proposed as an efficient method for a rapid prediction of the global mean flow in stirred reactors. Various aspects of the simulation results were assessed: quality of the fluid prediction, computational requirements, existence of numerical problems and availability of crystal size distribution. The developed Smoothed Particle Hydrodynamics CFD model was successfully coupled with discretised population balance equations to model a cooling batch crystallization process. It has been shown that 200 additional transport equations resulting from the discretisation of the population balance leads to only 50% decrease in computational performance while the same problem is still almost intractable from the computational point of view using the grid-based CFD methods.
1 citations
TL;DR: Compared with the RKPM, the RRKPM has higher computational accuracy and better stability, and the discretized system equation can be obtained using the integral weak form.
Abstract: In this paper, the method of radial basis function (RBF) is employed to construct the approximating function of the reproducing kernel particle method (RKPM), which can reduce the adverse effect of different kernel functions on computational accuracy and improve stability in the problem domain, and the radial basis reproducing kernel particle method (RRKPM) is presented. Compared with the RKPM, the RRKPM has higher computational accuracy and better stability. Then RRKPM is applied to wave propagation, and the discretized system equation can be obtained using the integral weak form. The penalty method is applied to imposing the essential boundary condition, and the two-point difference method is selected to discretize the time. The accuracy and stability of the RRKPM for wave propagation problem are illustrated by the numerical examples.
1 citations
10 Jun 2019
TL;DR: A new adaptive scheme for solving elliptic partial differential equations (PDEs) through a radial basis function (RBF) collocation method that is meshless and characterized by the use of an error indicator, which depends on a leave-one-out cross validation (LOOCV) technique.
Abstract: We present a new adaptive scheme for solving elliptic partial differential equations (PDEs) through a radial basis function (RBF) collocation method. Our adaptive algorithm is meshless and it is characterized by the use of an error indicator, which depends on a leave-one-out cross validation (LOOCV) technique. This approach allows us to locate the areas that need to be refined, also including the chance to add or remove adaptively any points. The algorithm turns out to be flexible and effective by means of a good interaction between error indicator and refinement procedure. Numerical experiments point out the performance of our scheme.
1 citations
TL;DR: A geometrically nonlinear total Lagrangian Galerkin mesh free formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam is proposed in this paper.
1 citations