Determining Mesh Quality and Accuracy Parameters
Key Takeaways:
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The quality of a mesh (measured by geometric metrics for each cell in the mesh) influences the accuracy and convergence of the CFD solution.
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There are several common metrics that are widely used to assess mesh quality but still more that are unique to the CFD flow solver in which the mesh will be used.
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The degree to which the boundary layer flow is resolved is indicated by a parameter called Y+.
In CFD modeling, mesh generation is a complicated yet important process in complex numerical computation. In a fluid system, mesh breaks down the 3D model into thousands of smaller flow domains where the governing equations can be discretized and resolved for each domain. The quality of the mesh generated plays an important role in ensuring the accuracy and stability of the simulation results.
Since meshing is one of the bottlenecks in the simulation process, ensuring the mesh is of high quality is important for fast and accurate analysis. For mesh quality assessment, it is necessary to understand the criteria that dictate this analysis. CFD solvers can help engineers in this analysis through mesh quality evaluation and error estimation.
Metrics for Mesh Quality Evaluation
In fluid system simulation, the challenge starts with the system geometry. Mesh simply enables discretization of the geometry to ensure all relevant flow features are captured uniquely in each cell. This can, however, be challenging given the complexity of the domain, the complexity of the geometric model, and the type of mesh desired. For instance, it is much easier to generate simple cells like triangles than cubicle or hex meshes. The error developed during the process is generally accounted to:
- High skewness
- Incorrect boundary layer meshing
- Coarse meshing
- A large aspect ratio leading to interpolation error
Addressing these errors is the main goal of mesh quality analysis. Regardless of the mesh types being used, the following common metrics for mesh quality should be understood to minimize mesh quality issues.
Node Point Distribution
When establishing a flow domain, the mesh should satisfy node distribution requirements. This is necessary to make sure that flow features, such as mixing zones, flow layers, separated regions, boundary layers, and wakes, are accurately represented. Poor resolution in such areas can alter the flow characteristics within the simulation. At the boundary layers, node distribution can impact the accuracy of the shear stress and heat transfer coefficient.
Due to its erratic behavior, the computational analysis of turbulent flow is more complex than laminar flow. Thus, its accuracy relies more on mesh quality. The same is true for near-wall regions; depending on the fluid attributes and near-wall model being used, mesh resolution can vary.
It is recommended to have fine meshes in regions where there is a rapid change in mean flow to minimize the effect of change in flow variables.
Smoothness
During mesh generation or refinement, it is necessary for the change in cell size to be smooth. Any sudden jump in cell size can result in an error. Ideally, the change in size between the two adjacent meshes should be less than 20%. A good smoothness, with uniform angular transition, is highly desirable in simulations, as it enables an accurate interpretation of the model.
Skewness
Skewness is one of the primary indicators of mesh quality. In the interpolated regions, highly skewed cells can decrease the accuracy of the numerical solution. The skewness parameter can be determined using the following methods:
Equilateral volume
This is a default skewness analysis method for triangles and tetrahedral.
Deviation from the normalized equilateral angle
This equation holds true for prisms and pyramids and applies to all types of faces or cells.
Equiangular skewness
Where,
- 𝛳max: largest angle in the cell, in degrees
- 𝛳min: smallest angle in the cell, in degrees
- 𝛳e: angle for equiangular cell, (i.e., 90 degrees for rectangle, 60 degrees for triangle)
In general, for quality mesh, skewness values for different mesh types should not exceed:
- Hexahedron and quadrilateral cells: 0.89
- Triangle cells: 0.89
- Tetrahedral cells: 0.9
When determining the mesh quality, it is important to make sure these parameters of smoothness, skewness, and node density hold true. With inaccurate mesh quality, it is possible that the simulation may converge or diverge and provide inaccurate results.
Resolving Boundary Layer Flow With the Y+ Parameter
Near the boundary layers, almost all types of flow exhibit a similar pattern. In such a case, Y+ enables the identification of the point of calculation in the boundary layer profile. Y+ is a dimensionless parameter that accurately represents the near-wall region by indicating the measurement of the distance from the wall of the fluid system. It is often used with importance in turbulence modeling where it captures wall-bound turbulence by enabling the calculation of cell size near domain walls.
Creating High-Quality Mesh in CFD Simulators
CFD simulators can create a highly detailed mesh for an accurate representation of a 3D model for high fidelity simulation. Through the appropriate choice of mesh type and the fulfillment of accuracy parameters, you can ensure high-quality meshing, whether the assessment is done before running the simulation or once the issue is encountered during simulation.
With CFD solutions from Cadence it is possible to auto-generate suitable meshes with the desired degree of fineness for analysis of a wide range of flow geometries. Through seamless mesh generation and accurate analysis of mesh quality, it is possible to minimize computational errors while improving your workflow.
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