An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques

Seven Cases Unstructured Triangulation Technique for Simplified Version of Conceptual Model of Ethylene Furnace for Radiative Heat Transfer Approximation

In this paper, we introduce a new enhanced method utilizing the approach of advancing front technique for generating unstructured meshes in the simplified version of ethylene conceptual model. The method is called as Seven Cases Unstructured Triangulation Technique (7CUTT) where it is based on seven categories of cases for element creation procedure and the layer concept for mesh gradation control. The algorithm of the mesh incorporates sensor deployment in its conceptual model to supply input for boundary values. The quality of the mesh is determined based on a measurement in GAMBIT software. 7CUTT provides the framework for the heat to be approximated using the discrete ordinate method, which is a variant of the finite volume method. Simulation results produced using FLUENT support the findings for effectively approximating the flue gas temperature distribution in the simplified furnace at the end of the study

Micro-Macro relations for flow through random arrays of cylinders

The transverse permeability for creeping flow through unidirectional random arrays of fibers with various structures is revisited theoretically and numerically using the finite element method (FEM). The microstructure at various porosities has a strong effect on the transport properties, like permeability, of fibrous materials. We compare different microstructures (due to four random generator algorithms) as well as the effect of boundary conditions, finite size, homogeneity and isotropy of the structure on the macroscopic permeability of the fibrous medium. Permeability data for different minimal distances collapse when their minimal value is subtracted, which yields an empirical macroscopic permeability master function of porosity. Furthermore, as main result, a microstructural model is developed based on the lubrication effect in the narrow channels between neighboring fibers. The numerical experiments suggest a unique, scaling power law relationship between the permeability obtained from fluid flow simulations and the mean value of the shortest Delaunay triangulation edges (constructed using the centers of the fibers), which is identical to the averaged second nearest neighbor fiber distances. This universal lubrication relation, as valid in a wide range of porosities, accounts for the microstructure, e.g. hexagonally ordered or disordered fibrous media. It is complemented by a closure relation that relates the effective microscopic length to the packing fraction

The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes

The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smoothing for tri-quad meshes. When smooth surface meshes, for trian-gular, quadrilateral and quad-dominant mixed meshes, the mean quality(MQ) of all mesh elements always increases and the mean square error (MSE) decreases during smoothing; For tri-dominant mixed mesh, the quality of triangles always descends while that of quads ascends. Test examples show that the MDM is convergent for both planar and surface triangular, quadrilateral and tri-quad meshes.Comment: 18 page