Partially Overlapping and Conforming Mesh Blocks
This development note written by Michael Barkhudarov, Ph.D., VP of R & D and Arun Jose, Ph.D., Developer, discusses a new meshing technique to be included in the 2014 release of FLOW-3D.
The free gridding technique in FLOW-3D consists of a structured rectangular mesh combined with the Fractional Area/Volume Obstacle Representation (FAVOR™), offering the user the inherent simplicity and robustness of a rectangular mesh, accurate geometry representation and the flexibility of independently changing the mesh or the geometry.
Over the years the meshing algorithm has been extended to multi-block meshes and Unstructured Memory Allocation (UMA) for increased power to capture complex flow domains. This article describes further advances in FLOW-3D’s meshing capabilities in the form of conforming and partially overlapping mesh blocks.
Conforming Mesh Blocks
Most metal casting applications are characterized by a mold cavity, where metal flow takes place, surrounded by a large solid mold where only heat transfer equations are solved. Casting large complex parts typically requires fine mesh resolution in the cavity, but the thermal solution in the mold is far less demanding of the grid quality. High pressure die casting (HPDC) of an automotive door or instrument panel is a good example of such disparity in scales: a door is typically 1 or 2 mm thin, while the die can be over a meter across. Using rectangular mesh blocks for such cases requires a significant investment of the user’s time and ingenuity to fit the computational domain into the computer’s memory. Even then it is hard to completely eliminate fine mesh where it is not needed.
A conforming mesh block is designed to address these issues by resolving only the cavity and a uniform layer of solid around it. Cells outside that layer of mold material are discarded from the simulation and computer memory. The solid part of the mold is then enmeshed with another, coarser, containing block.
The result is a compact two-block mesh for the cavity and the mold that delivers an efficient and accurate solution in both domains. Figure 1 shows a slice through a simple mold with an overlaid two-block mesh. The fine mesh is located in and immediately around the cavity (and a cooling channel), while the coarse mesh extends to the rest of the mold. The thermal solution in the solid is then transferred between the two mesh blocks at the boundary.
The only user-adjustable parameter for a conforming mesh block is the extent of the overlap into the solid. This parameter is defined in terms of the thickness of the overlap layer in the direction normal to the cavity wall. By default, a conforming block overlaps the solid by five cells.
The overlap region is necessary not only to facilitate the transfer of the thermal solution in the solid between the blocks, but also to better capture the large temperature gradients in the solid in the vicinity of the cavity surface.
Partially Overlapping Mesh Blocks
FLOW-3D offers the capability to handle multiple mesh blocks using linked and nested blocks. One feature that has been requested by FLOW-3D users is to extend this capability to allow partially overlapping mesh blocks. This would allow additional flexibility in problem set up and facilitate the use of fewer blocks for certain types of problems because the user does not have to ensure that meshes are perfectly aligned at their mutual boundaries.
When two meshes overlap partially, the solution is computed only on one mesh while the grid cells in the other mesh are deactivated in order to avoid storing data and solving the governing equations for both meshes in the overlap region. By default, the grid having a higher resolution is used to compute the solution in the overlap region. The user can override the default behavior by setting mesh priority/rankings to specify which mesh to activate in the overlap region. Figure 3 shows an example where four partially overlapping mesh blocks within a single main mesh block are used to accurately capture the inflow into a reservoir with eight inlets. This problem would have required twice as many blocks if it were solved using only nested and linked blocks. The fluid has been colored differently in different regions to indicate the mesh block that is active in that region. Figure 4 shows the top view for the same problem.
Together with the addition of solution sub-domains, where solution space for each variable is compactly allocated, conforming mesh blocks allow users to run ever larger simulations on desktop computers. For example, a billion cell HPDC simulation for the door shown in Fig. 2 using the single precision solver would require less than 100 GB of memory. The ability to handle partially overlapping mesh blocks provides additional flexibility and convenience to the user.
In the future, the concept of conforming mesh blocks can be extended to other geometric constraints such as a user-defined region of special interest in the computational domain. The addition of partially overlapping mesh blocks is currently more of a user convenience than a solution enhancement, but it paves the way to allowing mesh blocks to move which would be a qualitative leap in FLOW-3D’s meshing capabilities.