Reliable isotropic tetrahedral mesh generation based on an advancing front method

In this paper, we propose a robust isotropic tetrahedral mesh generation method. An advancing front method is employed to control local mesh density and to easily preserve the original connectivity of boundary surfaces. Tetrahedra are created by each layer. Instead of preparing a background mesh for mesh spacing control, this information is estimated at the beginning of each layer at each node from the area of connecting triangles on the front and a user-specified stretching factor. An alternating digital tree (ADT) is prepared to correct the mesh spacing information and to perform geometric search efficiently. At the end of the mesh generation process, angle-based smoothing and Delaunay refinement are employed to enhance the resulting mesh quality. Surface meshes are prepared beforehand using a direct advancing front method for discrete surfaces extracted from computed tomography (CT) or magnetic resonance imaging (MRI) data. The algorithm is demonstrated with several biomedical models

Image-Based Pore-Scale Modeling of Inertial Flow in Porous Media and Propped Fractures

Non-Darcy flow is often observed near wellbores and in hydraulic fractures where relatively high velocities occur. Quantifying additional pressure drop caused by non-Darcy flow and fundamentally understanding the pore-scale inertial flow is important to oil and gas production in hydraulic fractures. Image-based pore-scale modeling is a powerful approach to obtain macroscopic transport properties of porous media, which are traditionally obtained from experiments and understand the relationship between fluid dynamics with complex pore geometries. In image-based modeling, flow simulations are conducted based on pore structures of real porous media from X-ray computed tomographic images. Rigorous pore-scale finite element modeling using unstructured mesh is developed and implemented in proppant fractures. The macroscopic parameters permeability and non-Darcy coefficient are obtained from simulations. The inertial effects on microscopic velocity fields are also discussed. The pore-scale network modeling of non-Darcy flow is also developed based on simulation results from rigorous model (FEM). Network modeling is an appealing approach to study porous media. Because of the approximation introduced in both pore structures and fluid dynamics, network modeling requires much smaller computational cost than rigorous model and can increase the computational domain size by orders of magnitude. The network is validated by comparing pore-scale flowrate distribution calculated from network and FEM. Throat flowrates and hydraulic conductance values in pore structures with a range of geometries are compared to assess whether network modeling can capture the shifts in flow pattern due to inertial effects. This provides insights about predicting hydraulic conductance using the tortuosity of flow paths,which is a significant factor for inertial flow as well as other network pore and throat geometric parameters

Body-fitting Meshes for the Discontinuous Galerkin Method

Abstract In this dissertation, a scheme capable of generating highly accurate, body fitting meshes and its application with the Discontinuous Galerkin Method is introduced. Unlike most other mesh generators, this scheme generates meshes consisting of quadrilateral or hexahedral elements exclusively. The high approximation quality is achieved by means of high order curved elements. The resulting meshes are highly suited for the application with high order methods, specifically the Discontinuous Galerkin Method, as large portions of the mesh are fully structured while matching the high order of the numerical method with a high order geometry representation at object and domain boundaries. The mesh scheme works in two steps. It chooses an interior volume that can be represented using a fully structured Cartesian mesh and connects it to the embedded objects and domain boundaries with a so called buffer-layer in a second step. Inside the layer, high order curved elements are applied for yielding high geometric representation accuracy. The resulting meshes are ideal for the application of high order methods. In the interior part the Cartesian structure can be exploited for obtaining high efficiency of the numerical method while the accuracy potential can be realized also in the presence of curved objects and boundaries. After introducing the mesh scheme, the Discontinuous Galerkin Method is described and applied for solving Maxwell’s equations. As a high order method it achieves exponential convergence under p-refinement. It is shown that using meshes produced by the novel scheme this property is achieved for curved domains as well. As an example, optimal convergence rates are demonstrated in a cylindrical cavity problem. In another example, the abilities of the method to produce correct spectral properties of closed resonator problems are investigated. To this end, a time-domain signal is recorded during the transient analysis. After applying the Fourier transform accurate frequency spectra are observed, which are free of spurious modes