Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical methods and computational science to solve and analyse problems involving fluid flows. CFD models are used to simulate the behaviour of fluid flow (liquids and gases) and their interactions with various surfaces.
A crucial part of setting up a CFD simulation is the creation of a mesh, which is the division of the computational domain into small, discrete cells or elements. This process is also described as the discretization of the geometry into a mesh. Virtual prototype of an anaerobic digester implemented by Modela. (a) digester domain, (b) implemented mesh, and (c) lateral views of the mesh.
The mesh plays a critical role in CFD simulations as it directly influences its accuracy, stability, and computational cost. A well-constructed mesh can accurately capture the complexities of the flow, leading to reliable simulation results. Conversely, a poorly designed mesh can result in significant errors, making the simulation less trustworthy.
For each cell of the mesh, the transport phenomena equations of the model must be solved in order to simulate the process in question. The implementation of the mesh is crucial to properly solve this system of equations, whether it is to simulate the dispersion rate of an industrial effluent, residence time in an agitated tank, or the airflow efficiency of diffusers. Virtual prototype of a stirred tank. (a) tank domain, (b) implemented mesh (sectional view), and (c) views of the mesh, other sectional plane and upper view. Source: Sadino‐Riquelme, M. C., Rivas, J., Jeison, D., Donoso‐Bravo, A., & Hayes, R. E. (2022). Computational modelling of mixing tanks for bioprocesses: Developing a comprehensive workflow. The Canadian Journal of Chemical Engineering, 100(11), 3210-3226.
At Modela, we understand how important the quality of the mesh is for the success of our virtual prototypes. Its implementation requires adherence to objective quality metrics, allowing our simulations to be both accurate and stable. However, the unique challenge presented by each geometry means there is no one-size-fits-all approach to mesh creation. This lack of standardisation demands exceptional creativity, patience and skill.
And yet, this investment of creativity and patience is richly rewarded, both in terms of solutions and proposals for our clients and in terms of the unexpectedly beautiful patterns that the modelling can yield.
This pair of butterflies appeared in a recent prototype for a mechanical agitator and served as a beautiful reminder of our driving force, to advance sustainability efforts across the industry.
So, the mesh is both an art and a science.
Virtual prototype of a portion of the sea in the north of Chile, implemented by Modela. (a) views of the sea domain, and (b) views of the mesh, from above and at the bottom.
FAQs
1. How do you determine the optimal size mesh cells to balance accuracy and computational cost, especially for complex geometries?
The process of determining the optimal size of mesh cells is a critical step in ensuring the accuracy and efficiency of Computational Fluid Dynamics (CFD) simulations. For complex geometries, we start by identifying areas where fluid flow variations are expected to be significant. In these regions, smaller cells are used to capture detailed flow patterns accurately. Conversely, larger cells can be applied in areas with minimal flow variation to reduce computational demand. This approach, known as mesh refinement, is guided by preliminary simulation results and a theoretical understanding of the fluid dynamics involved. Techniques like adaptive mesh refinement, where the mesh adjusts dynamically based on flow characteristics, are also employed to optimize the balance between accuracy and efficiency.
2. What specific metrics are used to evaluate the quality of the mesh, and how do these metrics influence the outcome of the simulation?
Several metrics are crucial for evaluating the quality of the mesh in CFD simulations. These include objective indicators for skewness, aspect ratio, and orthogonality, among others.
- Aspect Ratio evaluates the elongation of a cell, where a high aspect ratio may lead to numerical diffusion errors.
- Skewness measures how far a cell deviates from the ideal shape, which could affect the accuracy of gradient calculations within the cell.
- Orthogonality assesses the angle between faces and edges of cells, as angles far from 90° can impair the precision of the results.
Adjustments are made based on these metrics to improve mesh quality, directly influencing the simulation’s outcome by enhancing accuracy and reducing numerical errors.
3. Can you provide examples of how a well-constructed mesh has directly impacted the success of a particular project or simulation, highlighting the challenges and solutions encountered?
An example would be a project aimed at assessing the design of an industrial diffuser for the discharge of brine. The carefully designed mesh enabled us to accurately simulate the dispersion of the plume. By implementing a refined mesh with smaller cells in areas around the effluent discharge points, we could capture the complex flow patterns and the buoyancy of the plume. This level of detail allows for proposing design and operational modifications that could significantly improve the efficiency of the plume dispersion and, as a result, ensure a minimal impact to the environment.