Grid Generation Flashcards
Explain the Finite Difference Method
- Approximates the differential terms of a governing equation with finite difference equivalents. These finite differences are applied to discrete points in the domain.
What is the process of representation of the domain by a series of discrete points called?
Grid Generation.
What two factors influence the accuracy of approximation in the Finite Difference Method?
- the number of points (the distance between the points)
- choice of finite difference representation or scheme also influences the approximation error (order of approximation).
What are the 3 methods of discretization of the first derivative?
Method 1: Heuristic
Method 2: Comparison of Polynomials
Method 3: Combination of Taylor Series
Define Mesh Generation (FVM and FEM)
What about the special case of finite element based control volumes?
- The discretization of the domain in nodes where solutions is to be obtained.
- In FEM: the nodes are connected to form elements.
- In FVM: the nodes are centroids of control volumes.
- In CFX, it is a finite element based control volumes. control volumes are formed from an initial discretization with elements.
What are the three main types of grids? Explain each of them.
- Orthogonal (cartesian) grids AKA structured
- simplest to program
- very limited use
- codes that use this grid: Cart3D - NASA, AMR - Non-orthogonal (boundary fitted) grids
- When grid lines are aligned with the flow, numerical diffusion caused by UDS is minimized.
- structured grids are harder to generate when the geometry is not very regular, but they are usually suited best for flow calcs with high Re. - Unstructured grids:
- has larger artificial diffusion than a structured mesh
- it is typically less efficient to solve
- HOWEVER, the time it takes to prepare an adequate grid is much less.
What is the purpose of using mesh inflation?
- It is a resource that permits some alignment with the flow in an unstructured grid.
- the grid surfaces parallel to the wall will tend to be aligned with the boundary layer of the flow.
How to check the quality of an unstructured grid?
After generating a grid, verify the quality of your grid discretization in CFX-Post and calling the Mesh Calculator panel.
- The Mesh Calculator evaluates several grid quality parameters (edge length ratio, max face angle, min face angle, element volume ratio, connectivity number) and creating a corresponding variable that can be plotted in order to identify problem regions which may require re-meshing.
What are some qualities to look at with meshing?
- Aspect Ratio (longest side)/(shortest side), ideally <10
- Max/Min face angle: as close to 90 degrees as possible (or 60 degrees).
- Element Volume Ratio: size ration of one CV to the next. (ideally: 1.1 - 1.5)
- Skewness: as small as possible (<0.8)
- Orthogonal Quality: as close to 1 as possible (>0.2).
Explain Mesh Refinement
- Truncation error in the domain discretization is proportional to the grid spacing.
- It is possible to increase the accuracy of a solution by reducing the grid spacing.
- This can be accomplished in a global sense by setting the maximum edge to a smaller value.
- Often, the error is only larger in smaller regions, where there is steep gradients of the dependent variables (velocity gradient).
- An overall refinement would require a lot of computational power and would mean that large regions of the domain, with solutions not changing rapidly, are being “overly” accurately solved.
What does an ideal mesh provided (in terms of truncation error)
An ideal mesh provides evenly distributed truncation errors.
What is local mesh refinement?
- Used when only part of the total flow domain requires a finer mesh.
- If a uniform discretization scheme were used, regions of slow changes in the dependent variables would be wastefully refined, increasing unnecessarily the memory and computing time requirements.
Structured grids and local refinement
- Harder to implement local refinement in structured grids BECAUSE there are implicit connectivities required by the grid structure.
Unstructured grids and local refinement
Unstructured grid generators lead themselves to natural local refinement by the simple addition of nodes in the refinement region:
1. define which regions are to be locally refined
2. set an expansion factor or growth rate so that the element edge can gradually grow to meet the size of the larger length scale.
What happens if the Expansion Factor is too large? (>1.3)
The second order convergence of CDS type of discretization schemes will be lost.
What happens if the Expansion Factor is too small?
The expansion will take up too much space and be carried deeper into the domain than necessary, thereby wasting computational resources.
What expansion rate value is ideal?
Between 1.0 and 1.3.
What are hex-dominant meshes?
They are hybrid meshes with unstructured meshes close to the complex geometries, then transitioning into regions of structured mesh away from the complex geometry.
What is adaptive Meshing?
It is the automatic refinement of the grid based on preliminary solutions, which indicate the code where the regions of higher truncation error are.
Explain the steps of Adaptive Meshing
- Calculation of a preliminary solution on a coarse grid.
- Calculation of error estimates (adaption criteria) throughout the domain and identification of regions with higher error than a certain threshold.
- Remeshing with addition of the appropriate number of nodes in the selected regions, according to the level of error estimator (error indicator).
- Interpolation of solution from coarser grid onto the refinement grid to serve as initial condition.
- New calculation of the solution with the refined grid.
- Repeat from step 2 until overall error estimates satisfy convergence criteria.
