Five questions about the computational grid

: Last Updated: 10 August 2021

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In this article we will be discussing the computational grid. FlowVision uses a structured locally adaptive mesh with sub-grid resolution of geometry, predominantly consisting of hexagonal cells. The computational grid is constructed automatically. The accuracy of the mesh refinement of a geometric model of any complexity is ensured by using a technology for sub-grid geometry resolution.

If you would like to know more, read on for our answers to the 5 most frequent questions about the FlowVision grid:

1. How to construct a computational grid in FlowVision?
2. What is "adaptation" of the computational grid?
3. How to evaluate mesh quality in FlowVision?
4. I have a complex geometric model. How can the FlowVision mesh ensure accuracy of the calculation in boundary cells?
5. The computational grid and moving bodies: how do they interact during the computation process?

FlowVision uses a structured locally adaptive mesh with sub-grid resolution of geometry, predominantly consisting of hexagonal cells

The main feature of the computational grid FlowVision is the speed with which it is generated. The user only needs to specify the number of grid lines in each Cartesian coordinate direction (to build a uniform grid) or specify the cell size and refinement reference lines in the initial-grid editor (to build a non-uniform grid). After that, the program will quickly automatically generate the mesh.

Uniform mesh (left) and non-uniform mesh with increased density near the profile (right)

Adaptations are used to refine the mesh cells in order to get a more accurate local solution. In FlowVision you can adapt the mesh on boundary conditions, as well as on the surface or within the volume of geometric objects. Conditional adaptation or adaptation to solution can be used to adapt the mesh based on local key parameter values within the simulation. Adaptation can be used not only to refine the mesh, but also to undo the splitting of cells (up to the initial level) - this is called merging. Merging of adaptations allows the use of dynamic adaptation methods that change throughout the simulation process. This approach allows you to, throughout the calculation, resolve (refine) only those regions containing parameter values of interest, while conserving computational resources (in areas where adaptation is no longer needed, it will be removed by merging the cells).

A more precise resolution of the viscous boundary layer is made possible by the subsurface mesh. This technology helps achieve detailed mesh refinement in the near-wall region along with significant computational savings when compared to regular 3D adaptation.

It may seem that refinement of the computational grid is a necessary condition for obtaining an accurate, precise solution in CFD solvers. But in FlowVision this is not always the case. For example, by using the gap model, it becomes possible to obtain an accurate solution in narrow channels and gaps without the need for mesh refinement.

HOW TO CONSTRUCT A COMPUTATIONAL GRID IN FLOWVISON?

Generating the initial grid in FlowVision is easy. The grid is constructed automatically in accordance with the specified parameters which can be either the number of lines of uniform division in each Cartesian direction, or the cell size and the position of refinement lines for higher grid density.

You can see the ease of meshing in FlowVision for yourself in this vi deo about working with the Initial Mesh Editor.

After building the initial mesh, adaptations can be used to refine it locally in order to improve the accuracy of the results. Alternatively, a boundary-layer grid can be applied: it is constructed based on the mesh present at the time of construction and then does not change throughout the simulation.

For local and parallel (MPI) computations, building the initial mesh requires different approaches

For calculations on a local computer, you can set a coarse initial grid, and then locally refine it during the calculation process. However, this means that in order to achieve the appropriate cell size near surfaces, a high level of adaptation (6-8) may be required.

For calculations via MPI, on the contrary, it is recommended to set a finer initial grid and then use an adaptation of no more than 3-4 levels. This is due to the fact that the distribution of the computational grid among processors is performed along the initial grid. Local refinement may then fall into one processor, resulting in an uneven load distribution among the processors which will slow down the parallel computation. Even so, FlowVision has a dynamic balancing function that reallocates cells across processors, ensuring that they have the same degree of utilization.

WHAT IS "ADAPTATION" OF THE COMPUTATIONAL GRID?

Grid adaptation is the splitting of mesh cells into smaller ones used for local solution refinement.

Adaptation can be applied to those areas of the computational domain in which it is necessary to refine the solution: for example, in the near-wall layer or in regions with steep gradients, etc. In FlowVision, you can adapt the mesh:

at the surface or within the volume of geometric objects (you can also further adapt sharp corners and curved surfaces – regions where the flow changes and large gradients appear)
at the surface of boundary conditions
in regions with large gradients of parameters or with a certain value of a specific parameter.

When standard 3D adaptation is enabled, the initial-level computational cells are split in half in all three directions, resulting in 8 smaller cells. Initial grid cells have adaptation level 0. With a single partition of the initial grid, cells with adaptation level 1 are formed. With further partitioning the adaptation level sequentially increases, accordingly.

A level 0 cell is adapted to level 3

Adaptation is not only the splitting, but also the combining of cells into larger ones (but not larger than the initial level 0 cell size). In FlowVision, this is called merging.

The combination of periodic merging and mesh refinement using adaptation by condition means you can have dynamic mesh adaptation in FlowVision. It then becomes possible to refine the mesh only in the areas that require finer mesh resolution for solution accuracy, whereas excess adaptation in the rest of the computational space merges back to lower levels on account of being unnecessary.

Dynamic adaptation by density in supersonic flow around a wedge: using adaptation by condition + merging

HOW TO ASSESS MESH QUALITY IN FLOWVISION?

Mesh quality is evaluated by performing a grid convergence study.

In our opinion, the only criterion to assess the quality of the computational grid is the quality of the results. You can only be sure in the quality of the obtained calculation result after having conducted a grid convergence study for the solution. The idea is that the cells of the computational grid are successively refined (“adapted”) and, for each level of adaptation, we record the value of a controlled parameter and the change in this value caused by refining the size of the cells.

Adapting the grid by just one level can cause the value of the controlled parameter to change by 20-30%! But with subsequent adaptations, this difference will become less and less significant, until at one point the solution will cease to be affected by the degree of mesh refinement entirely. This is the mesh that will then give a reliable, high-quality result.

It is faster and more convenient to carry out grid convergence studies in a 2D formulation of the problem and then use the obtained resulting grid for 3D calculations

I HAVE COMPLEX MODEL GEOMETRY. HOW CAN THE MESH IN FLOWVISION ENSURE SOLUTION ACCURACY IN BOUNDARY CELLS?

The exact replication of the geometric model surface by the computational mesh is ensured by using the sub-grid resolution method.

The sub-grid resolution method is applicable to geometry of any degree of complexity and detail. Sub-grid resolution does not simplify the model geometry, but simply changes the shape of the cells surrounding it. The model is subtracted from the automatically generated mesh and, for each boundary cell, fluxes are approximated across each cell face. Therefore, a boundary cell differs from a regular one only in that it does not have 6 faces, but more, depending on the complexity of the geometry.

Cells formed by subtracting the geometric model from the computational grid. The shape of the cell depends on the complexity of the geometry.

The most difficult thing in the method of sub-grid geometry resolution is solving equations in boundary cells with intricate shapes. Our developers successfully cope with this task by using finite volume approximation of equations.

This is how FlowVision combines the convenience of automatic mesh generation with the accuracy of sub-grid resolution to produce high-quality results

COMPUTATIONAL GRID AND MOVING BODIES: HOW DO THEY INTERACT DURING THE CALCULATION PROCESS?

FlowVision uses Euler's approach to mesh generation: the computational mesh is stationary, and the body moves along it.

Demonstration of Euler's approach: a "moving body" moving along the computational grid

First, the position of the object model is updated according to the applied laws of motion. Then, the object model geometry is subtracted from the computational grid. This process is repeated at each iteration.

The main difficulty in implementing this approach is that as the object moves through the space, cells of the computational grid disappear. But the fact that the mesh is not tied to the model geometry allows you to assign the body an absolutely arbitrary motion and simulate the full surface contact. Then, during the motion, the mesh is rebuilt only near the moving body, rather than over the entire volume of the computational space. This optimizes use of computational resources.

MOVING BODIES AND ADAPTATION

To resolve the near-wall layer of a body (whether it is moving or not), it is convenient and rational in terms of computational resources to apply mesh adaptation to the surface of this body. However, if you simply adapt the surface of a body that is in motion, then there will always be traces of adapted cells trailing behind it (as in the picture below). Merging will help remove unnecessary adaptation.

A trail of over-adaptation behind a moving cube. Use merging to optimize the computational mesh.

It is better to drain the trail of adaptation periodically, rather than at every step. Just like the unnecessary adaptation behind a moving body, frequent merging also consumes computational resources

Five questions about the computational grid

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HOW TO CONSTRUCT A COMPUTATIONAL GRID IN FLOWVISON?

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