Flow Balancing in Modeling of Multi-Phase Flow using Non-Conformal Finite Element Meshes

The method of balancing numerical finite element flows in modeling a process of multiphase flow using non-conformal hexagonal meshes is considered. Studies have been carried out for a simple reservoir configuration and on a more complex model of a real field of high-viscosity oil in the Tatarstan. The research results showed that the balancing method allows one to obtain a conservative solution when using non-conformal finite element meshes with sufficiently large cells. At the same time, this method is completely free of problems associated with grid orientation, even for complex models containing zones with highly variable permeability. The proposed algorithm for the adaptive choice of parameters allows to do the factorization of the SLAE matrix at sufficiently small number of time steps; therefore, the computational costs of the flow balancing procedure are an order of magnitude less than the costs associated with calculating the pressure field and phase transfer. The used non-conformal finite element meshes with an arbitrary number of docked hexagons can significantly reduce the number of degrees of freedom when modeling multiphase flows in reservoirs with much small local heterogeneity and in the presence of several perforated zones. As a result, computational costs are reduced by almost an order of magnitude, and, at the same time, the required approximation accuracy is maintained. With an increase in the scale of the model and the number of operating wells, this advantage increases even more.

A Study on Various Mesh Generation Techniques used for Engineering Applications

In this paper our aim is to provide a survey of mesh generation techniques for some Engineering applications. Mesh generation is a very important requirement to solve any problem by very popular numerical method known as Finite element method (FEM). It has several applications in various fields. One such technique is Automated generation of finite element meshes for aircraft conceptual design. It’s an approach for automated generation of fully connected finite element meshes for all internal structural components, given wing body, geometry model, controlled by a few conceptual level structural layout parameters. Another application where it is used is in the study of biomolecules to generate volumetric mesh of a biomolecule of any size and shape based on its atomic structure. These methods are proved to be a faster method due to the usage of computing techniques. Mesh generator is also used for creating finite element surface and volumetric mesh from 3D binary and gray scale medical images. Some of the applications include volumetric images, surface mesh extraction, surface mesh repairing and many more. It is of great importance in understanding the human brain which is a complex subject. Though 3D visualization is a useful tool available, yet it is inadequate due to its challenging computational problem. This paper also includes the survey on latest tools used for these applications which overcomes many problems associated with the conventional approaches.

3-D adaptive FEA with weighted node density technique

Purpose This paper aims to propose a method to create 3-D finite element meshes automatically using the Delaunay tetrahedralization with the weighted node density technique. Using this method, the adaptive finite element analysis (FEA) was carried out for the calculation of the magnetic field of an eddy current verification model to clarify the usefulness of the method. Moreover, the error evaluation function for the adaptive FEA was also discussed. Design/methodology/approach The method to create the 3-D finite element meshes using the Delaunay tetrahedralization is realized by the weighted node density technique, and Zienkiewicz-Zhu’s error estimator is used as the error evaluation function of the adaptive FEA. Findings The magnetic flux density vectors on the node in the error evaluation function for the adaptive FEA should be calculated with the weighted average by the reciprocal of the volume of elements. Originality/value This paper describes the method to create 3-D finite element meshes and the comparison among calculation methods of the magnetic flux density vectors on the node for the error estimator.