Element Method For Three-dimensional Problems Research Articles

B-spline wavelet boundary element method for three-dimensional problems

B-spline wavelet boundary element method for three-dimensional problems

About Verification of Wavelet-Based Discrete-Continual Finite Element Method for Three-Dimensional Problems of Structural Analysis Part 1: Structures with Constant Physical and Geometrical Parameters along Basic Direction

This paper is devoted to verification of so-called wavelet-based discrete-continual finite element method (wDCFEM), proposed by authors, for three-dimensional problems of local structural analysis. Formulation of the problem for three-dimensional structure with constant physical and geometrical parameters along so-called its basic direction, solutions obtained by wDCFEM and discrete-continual finite element method (DCFEM) and their comparison are presented. It was confirmed that wDCFEM is rather effective in the most critical, vital, potentially dangerous areas of structure in terms of fracture (areas of the so-called edge effects), where some components of solution are rapidly changing functions and their rate of change in many cases can’t be adequately taken into account by the standard finite element method.

About Verification of Wavelet-Based Discrete-Continual Finite Element Method for Three-Dimensional Problems of Structural Analysis Part 2: Structures with Piecewise Constant Physical and Geometrical Parameters along Basic Direction

This paper is devoted to verification of so-called wavelet-based discrete-continual finite element method (wDCFEM), proposed by authors, for three-dimensional problems of local structural analysis. Formulation of the problem for three-dimensional structure with piecewise constant physical and geometrical parameters along so-called its basic direction, solutions obtained by wDCFEM and discrete-continual finite element method (DCFEM) and their comparison are presented. It was confirmed that wDCFEM is rather effective in the most critical, vital, potentially dangerous areas of structure in terms of fracture (areas of the so-called edge effects), where some components of solution are rapidly changing functions and their rate of change in many cases can’t be adequately taken into account by the standard finite element method.

An efficient method for simulation of the dynamics of a large number of deformable droplets in the stokes regime

Direct simulations of the interaction of a large number of deformable droplets are necessary for more accurate predictions of rheological properties and the microstructure of liquid-liquid systems. In the present study, a mathematical model of a three-dimensional flow of a mixture of two Newtonian liquids of a droplet structure in an unbounded domain at low Reynolds numbers is considered. An efficient computational method for simulation of the dynamics of a large number of deformable drops is developed and tested. This approach is based on the boundary element method for three-dimensional problems accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). This enables direct simulations of systems of tens of thousands of deformable droplets on PCs, which is confirmed by test and demo computations. The developed method can be used for solution of a wide range of problems related to the emulsion flow in micro- and nanoscales. Also it can be used to establish the closing relations for simulation of two-phase liquid-liquid flow based on the continuum approach in macroscales.

Arbitrary Lagrangian–Eulerian methods for analysis of regressing solid domains and interface tracking

We present the details of the formulation and implementation of the arbitrary Lagrangian–Eulerian (ALE) finite element method for three-dimensional problems involving regressing solid domains and moving boundaries. An example of such problems is the simulation of solid-propellant rockets in which the evolution of a fluid–solid interface is governed by a combustion law and the transfer of mass and momentum across it. The ALE method, while providing a means to track the location of the interface, allows the adaptation of the finite element mesh to the constantly changing solid domain. In this study, the mesh adaptation is achieved via a novel smoothing technique in which the shape of finite elements with smaller volumes, which are more susceptible to mesh-entanglement, are better preserved compared to those with larger volumes. An analysis of the stability of the ALE computations, under certain simplifying assumptions, is also performed. The stability limits determined from this analysis can be utilized as constraints for adjusting mesh velocities or time increments in the convective mesh-motion phase of the ALE computations. In addition, a method is provided for generating verification problems with moving interfaces from those with known solutions on stationary material domains. A problem in which the prescribed growth of a cavity in an infinite medium under a time-varying pressure loading is used to verify the implementation and to demonstrate the verification technique.