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Mesh Generation in CFD
Abstract
A preprocessing step for the computational field simulation is the discretization of the domain of interest and is called mesh generation. The process of mesh generation can be broadly classified into two categories based on the topology of the elements that fill the domain. These two basic categories are known as structured and unstructured meshes. The different types of meshes have their advantages and disadvantages in terms of both solution accuracy and the complexity of the mesh generation process. A structured mesh is defined as a set of hexahedral elements with an implicit connectivity of the points in the mesh. The structured mesh generation for complex geometries is a time-consuming task due to the possible need of breaking the domain manually into several blocks depending on the nature of the geometry.
An unstructured mesh is defined as a set of elements, commonly tetrahedrons, with an explicitly defined connectivity. The unstructured mesh generation process involves two basic steps: point creation and definition of connectivity between these points. Flexibility and automation make the unstructured mesh a favorable choice although solution accuracy may be relatively unfavorable compared to the structured mesh due to the presence of skewed elements in sensitive regions like boundary layers.
In an attempt to combine the advantages of both structured and unstructured meshes, another approach in practice is hybrid mesh generation. In a hybrid mesh, the viscous region is filled with prismatic or hexahedral cells while the rest of the domain is filled with tetrahedral cells. It has been observed that a hybrid mesh in viscous regions creates a lesser number of elements than a completely unstructured mesh with a similar resolution. This type of mesh has no restrictions on the number of edges or faces on a cell, which makes it extremely flexible for topological adaptation. It is given that unstructured mesh has an advantage over the structured mesh in handling complex geometries, mesh adaptation using local refinement and de-refinements, moving mesh capability by locally repairing the bad quality elements, and load balancing using appropriate graph partitioning algorithms. In the case of a non-matched block-to-block boundary, interpolation issues have to be handled properly to satisfy the conservation principles. However, the structured mesh has a better accuracy for viscous calculations due to the fact that it can handle cells with very high aspect ratio cells in the boundary layer.
... The key to a successful CFD based simulation is the mesh generation (Sadrehaghighi, 2020), for a long time the usage of hexahedral elements was very popular as it showed great flexibility, the problem was that generating this kind of meshes was a complicated process that requires both time and experience, especially when dealing with complex geometries. Thus, hexahedral mesh generation continued to be difficult to perform and automate (Shepherd & Johnson, 2008). ...
... Convergence plot for the tetrahedral mesh model Convergence plot for the polyhedral mesh modelFor the overall calculation time, calculations based on the polyhedral meshes were almost three times faster than calculations based on tetrahedral meshes.2.2. Lift and drag coefficients:figures (8)(9) shows that both lift and drag coefficients started to converge after 100 iterations and fully converged after between (200-225) iterations, while figures (10)(11) shows that both coefficients in the tetrahedral mesh-based model started to converge after 200 iterations and fully converged only after between (1100-1200) iterations. ...
Meshing is one of the crucial key features to the success of CFD based simulations, this study is evaluating the efficiency of polyhedral elements in solving the problem of the flow around ship rudder, using a Reynolds-averaged Navier-Stokes turbulence model (SST k-ω), and compares it to a tetrahedral based mesh, considering that polyhedral elements were neglected in the past due to difficulties in implementing them, this was solved by introducing a tool by ANSYS that converges tetrahedral elements to polyhedral element, and integrating it into FLUENT software, the model was validated by comparing it with previously validated model which used the full version of ANSYS, this study was concluded using the academic version, but still it was able to produce satisfying results in predicting the lift and the drag coefficient, the pressure around the rudder surface, the velocity and the turbulent kinetic energy, finally the mesh quality was evaluated using the orthogonal quality criteria, the results showed the supremacy of the polyhedral elements in saving time and computational resources and improving mesh quality, and keeping high level of accuracy in predicting the results.
... The inflation meshing method (refined mesh with a special growth rate) was utilized near the side walls and around the pad patterns to capture the near-wall behavior accurately. 27,38,39 For the inlet and outlet regions of the domain, a sizing meshing method was applied, using Hexa-type meshes to ensure consistency and accuracy in these critical areas. Figure 4 illustrates the meshing structures in different parts of the computational domain. ...
This study explored the impact of micropattern designs on slurry dynamics in chemical mechanical planarization (CMP), focusing on pressure distribution, slurry flow and streamlines, abrasive residence time, and drag force. Using computational fluid dynamics (CFD) simulations, we examined how different pad patterns, including circle, triangle, square, ellipse, and square-circle, affect slurry behavior. It was found that the elliptical patterns caused the largest pressure drops due to their shape and arrangement, thus affecting material removal rates. Velocity analyses revealed that mean residence times and slurry flow velocities vary for different patterns, impacting the effectiveness of material removal. The results for the square-circle pattern showed a balanced slurry interaction, optimizing MRR by ensuring uniform slurry distribution and minimizing recirculation. The simulated drag forces exerted by the slurry on the pad patterns were correlated with the oxide removal rates. Particle tracking further illustrated how pattern design affects abrasive particle distribution, which is crucial for uniform polishing. The study identified the square-circle pattern as the optimal pattern design for TEOS film removal, highlighting the importance of pad pattern geometry in enhancing CMP efficiency. The presented simulation study highlighted the significance of micropattern design in advancing semiconductor manufacturing, offering insights for future pad design innovations.
... Therefore, the 42,886-mesh numbers are suitable for this case. Fig. 8 shows the visualisation of the 42,886-mesh numbers; the tetrahedral mesh configuration was uses because is more sensitive to stretching than polyhedral which benefits moving mesh (transient) features [28]. The 42,886-mesh numbers have a Δx of 1.7 mm, and the probe indicates that the average local velocity of fluid is 3.1 m/s. ...
... A boundary layer mesh is a semi-structured layered mesh around a given geometry. The early generation methods of boundary layer meshes are mainly PDE-Based methods, which have been widely used in early structured mesh methods [ 13,19,22,23]. Later, as the geometry model became more and more complex, the semistructured mesh gradually developed, and a separate boundary layer mesh concept was gradually formed, along with the unstructured mesh filled in between the boundary layer mesh and the bounding box. ...
Quadrilateral/prismatic boundary layer meshes are believed to combine precision with ease of use. However, the generation of full-layer boundary layer meshes without transition elements still needs to encounter the problem of robustness. This paper proposes a novel and robust full-layer boundary layer mesh generation scheme, which constructs an orthogonal target mesh and an extremely thin initial mesh and then iterates the initial mesh until its rigid mapping energy to the target mesh is minimal. A positive area/volume-preserving rigid mapping method is applied iteratively to ensure robustness. This method has been partly validated in 2D and has achieved preliminary results in 3D.
... Meshing is defined as a process to decompose the flow domain into a control volume where nodes are relative to the vertices and at each node the governing equation is applied in the solver phase. It is a pre-processing step for the computational field simulation where discretization of domain of interest is done [17]. ...
This thesis studies the effect of a rotating blade or swirl-meter on a column of fluid present beneath it in a simplified swirl-rig setup. The swirls and vortices created in the column of fluid were studied and analyzed computationally through the use of ANSYS software and experimentally through Particle Image Velocimetry (PIV).
... The structured mesh has equal number of adjacent elements as well as inner nodes, while the unstructured mesh does not follow the rule. The structured mesh contains hexahedra elements (3D) and squares (2D), and thus of the high quality of the elements due to its regular shape, this kind of mesh is widely used in research activities that are seeking better prediction results using CFD [10]. For example, there is evidence that Drag predictions based on RANS (Reynolds Average Navier-Stokes) equations using a structured mesh have a close approximation to the experimental data, much more than the predictions using unstructured or hybrid mesh. ...
The development of a methodology to simulate numerically the steady state flow field in Francis turbines was carried out using the open source CFD software OpenFOAM along with a MRF and AMI approach. A structured mesh obtained from previous studies was used with some modifications to solve the presence of imbalance points in the simulation. Numerical simulations using the SIMPLE algorithm were performed together with two different turbulence models. It was confirmed that the results obtained reproduced the phenomenon with a great approximation and predicted the output load with only a deviation of around 5.02% against experimental data.
The unmanned aerial vehicle (UAV) is becoming popular from last two decades and it has been utilizing in enormous applications such as aerial monitoring, military purposes, rescue missions, etc. Hence, the present work focused on the design of the UAV wing considering the CH10 airfoil. In this paper, the computational fluid dynamic analysis on CH10 cambered airfoil has been conducted to achieve the preliminary results on the aerodynamic lift and drag coefficients. The airfoil has a chord length of 1 meter and has been subjected to low Reynolds numbers of 500 000, which is the standard operating Reynolds number for UAV wing design. The C-type fluid domain has been constructed at 30C upstream and downstream of the airfoil to initialize the boundary conditions. The angle of attack ranging from 0° to 14° with the increment of 2° has been done by changing the direction of the freestream velocity. The aerodynamic characteristics have been numerically computed using Spallart-Allmaras and Transient SST models. The aerodynamic coefficients achieved by these two models have been validated based on the XFOIL data. The contours of static pressure and velocity magnitude at 0°, 5°, 10°, and 12° angle of attack have been portrayed. The static pressure distribution around the airfoil has been visually observed to analyze its influence on the aerodynamic coefficients. The velocity magnitude relation to the static pressure distribution has been approved based on Bernoulli's equation such that increasing velocity magnitude has decreased the static pressure. The present results show that the Transient SST model has shown better flow prediction for an airfoil subjected to low Reynolds number flow.
Computational Fluid Dynamics (CFD) is an important design tool in engineering and also a substantial research tool in various physical sciences as well as in biology. The objective of this book is to provide university students with a solid foundation for understanding the numerical methods employed in todays CFD and to familiarise them with modern CFD codes by hands-on experience. It is also intended for engineers and scientists starting to work in the field of CFD or for those who apply CFD codes. Due to the detailed index, the text can serve as a reference handbook too. Each chapter includes an extensive bibliography, which provides an excellent basis for further studies. The accompanying CD-ROM contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) as well as of grid generators. Provided are also tools for Von Neumann stability analysis of 1-D model equations. Finally, the CD-ROM includes the source code of a dedicated visualisation software with graphical user interface.
Validation studies often contains uncertainties due to boundary condition differences between computational fluid dynamics, CFD-, and experimental fluid dynamics, EFD-, in the setup for the cases involved. The present study is in two parts where the first part is a 2D parametric study of two geometrical parameters and their variation with blockage. The parameters were radius in the transition region from the windscreen to the roof and the angle of attack for the windscreen. A mesh blending technology has been used where an interpolation between two meshes is conducted on a vertices level for the creation of a mix between the two grids. Many CFD simulations have been done of which some are presented. The windscreen angle was more sensitive to blockage in the sense that trends in drag from two configurations may be erroneously predicted if large blockage is encountered. The front radius seems to be not so much sensitive in that respect and trends in drag and especially absolute drag levels changes only at very large blockage ratios. A separate study of blockage correction factors in the Volvo wind tunnel, hereafter-denoted PVT after its Swedish name, is ongoing, and for this study CFD simulations will be used for investigation of blockage effects for a full-scale car in this wind tunnel. The initial stage of this work which is more or less being able to simulate a slotted wall wind tunnel are presented. Comparisons are done with a car in a free stream, e.g. a very large solid wall wind tunnel.
A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the 'ideal' gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties.
The gradient calculation in the reconstruction phase is the key for the spatial accuracy and robustness of MUSCL type CFD schemes. For the gradient calculation, which bears central role in the second order reconstruction, new method for arbitrary polyhedra based on WLSQ (weighted least square) method merging the benefit of G-G (Green-Gauss) method is presented. The method, named GLSQ (G-G based WLSQ), has second order spatial accuracy for non-orthogonal and non-uniform linear mesh and gives rigorous gradient for thin curved mesh for which LSQ shows huge error. A new geometrical monotonicity condition, which gradient calculation method should satisfy for robustness, is also introduced. Although GLSQ is originally developed for hybrid meshes that combines octree and layered meshes, it is shown numerically that it also has better accuracy in usual rectangle and triangle meshes.
Geometry preparation and mesh generation are critical components of a CFD or other mesh based analysis process. The geometry definition and the mesh employed for a given computational analysis has a considerable impact on the quality, stability and resources expended to complete the predictions. Typically analysts spend a significant portion of their time on geometry and meshing issues, including frequent rework of a mesh generated and employed for an analysis. To properly model the problem the mesh boundaries must accurately represent the geometry of interest and non-geometric boundaries must form a suitable and closed domain of interest. The mesh must also consist of valid elements with appropriate spatial distribution. The suitability of a given mesh for accurately simulating the problem of interest is often referred to as 'mesh quality'. For complex geometrical configurations and complex physical processes the constraints are most severe. For example, poorly conditioned problems (i.e. stiff chemical kinetics, shocks etc.), non-linear, and/or transient analyses often place more severe demands upon mesh quality for useful simulations. In such cases, purely geometric metrics are incomplete. There are multiple methods employed for examining the quality of a mesh or an individual element. There is incomplete agreement upon the best metrics or even how to evaluate them. It is also widely acknowledged that that mesh quality ultimately depends upon the solution to the physical problem. Still, an a priori evaluation of the mesh quality that would provide some indication of the suitability of a particular volume discretization for the analysis to be performed would be very useful and would greatly benefit the analysis community. Mesh quality metrics could also be useful for defining improvements in mesh generation tools and processes. The objective of the workshop was to document, discuss and evaluate grid quality metrics in order to capture current practices and develop future strategies. © 2012 by the American Institute of Aeronautics and Astronautics, Inc.
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.