Abstract

Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industry. However, most computer programs used in the industry work in the frequency domain, with the subsequent limitation in the accuracy of their model predictions. The main objective of this work is the development of a time domain solver based on the finite element method capable of solving multi-body seakeeping problems on unstructured meshes. In order to achieve such an objective, several techniques are combined: the use of an efficient algorithm for the free surface boundary conditions, the use of deflated conjugate gradients, and the use of a graphic processing unit for speeding up the linear solver. The results obtained results by the developed model showed good agreement with analytical solutions, experimental data for an actual offshore structure model, as well as numerical solutions obtained by other numerical method. Also, a simulation with sixteen floating bodies was carried out in a affordable CPU time, showing the potential of this approach for multi-body simulation.

Abstract

In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration (SLI); and the second one based on the Streamline-Upwind Petrov-Galerking (SUPG) stabilization. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.

Abstract

This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown.

Abstract

There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied. 

Abstract

Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures 1) the Control Volume Function Approximation (CVFA), and 2) the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate.

Abstract

Abstract

The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development of reservoirs and well boring process. The mathematical formulation is based on the theory of repeated superposition of large deformations. A numerical discretization of the posed boundary problems of interacting solids is performed using a discontinuous spectral element method and multi-point constraints at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which significantly reduces the computational costs when conducting numerical modeling and lowers the requirements to the model preprocessing and mesh quality. The considered approach allows predicting in more detail the behavior of the rock during reservoir development, taking into account different stages of the field deformations. In particular, the redistribution of accumulated deformations during multistep loading and / or changes in the structure (topology) of the loaded body, as well as contact conditions of adhesion / sliding at the interlayer boundaries and bonded contacts are taken into account. These problems were solved using CAE Fidesys software, which allows solving static and dynamic problems of geomechanics and geophysics using finite (FEM) and spectral (SEM) element methods of a variable approximation order in space at non-conformal unstructured meshes.

Abstract

Abstract

The paper presents a method for simulating the flow of a viscous compressible gas around a moving obstacle, specified by the immersed boundary method on a simply connected unstructured mesh, and the features of its application for bodies of different configuration. An advantage of the developed moving-mesh method is that it keeps the topology of an initial mesh and provides an anisotropic mesh refinement to the 'immersed' surface of a streamlined body. The position and shape of the body are determined by the interpolation grid, which stores the distance and normal to the body surface. The paper also describes a special technique to improve the efficiency of adaptation. The technique is based on the prediction of the body location in some automatically chosen time. This trick allows to find the coordinates of mesh vertices during the predicted time interval by interpolation. The integral strategy combining the immersed boundary method with the developed moving-mesh adaptation is tested on several model cases in twoand three-dimensional formulations. However, the paper does not consider the numerical results of the cases, it is mostly targeted at the meshing details.