I recently had an inquiry from a customer who is using HiPhi to model a complex switchyard with lots of wires, poles and electrodes. He felt that there were problems in the program because he got error messages when he tried to implement the Boundary method to create a high-accuracy solution in a local volume. I found that the problems resulted from flaws in the global solution. The customer had specified volumetric models with surface fitting for every narrow wire and pipe in the assembly. Even with a large mesh of seven million elements, the representations of the wire cross-sections were marginal, resulting in thousands of corrected elements. In turn, implementation of the Boundary method involved thousands of field interpolations in the global solution to set surface potentials. There was a high probability of encountering at least one error while searching for elements or performing least-squares fits.
In this note I will give some guidelines for using node rather than volumetric models in MetaMesh to represent thin objects in electrostatic solutions. (In the MetaMesh manual, the two types are referred to as Open and Filled models respectively). I will use the calculation shown in the first picture as an illustration. Two electrodes are suspended inside a grounded box by thin rods. The spherical electrodes have radius 2.0 cm and the connecting rods have radius 0.2 cm. The electrodes on the right have potential +25 kV, while the electrodes on the left are at potential +10 kV. Beginning users often take a literal approach and try to represent all objects in such an the assembly with fitted volumetric models. This brute-force approach may lead to distorted elements, inaccurate results and long run times.
As I have pointed out many times in this blog, it is always a good idea to plan a strategy for the calculation before starting work on the computer. In the example, suppose that our main concern is the field distribution between the spherical electrodes. In this case, the critical fields are almost unaffected if the supporting wires have zero radius rather than a small radius. Therefore, we can consider the option of using node models for filaments to represent the wire. This choice reduces the workload for MetaMesh. To implement the node Line model, the program simply shifts individual vertices to lie close to the specified path. In contrast, to create a volumetric Cylinder, MetaMesh must identify elements that lie inside the shape boundary and then shift selected nodes toward the theoretical surface. The process is sensitive to the choice of element size and involves an order of magnitude more work. Consequently, there are more chances for errors.
In the example wiredemovolume.min, I used the Cylinder model with fitted surfaces for the connecting wires. For an accurate representation, I had to use an element size of 0.10 cm over the volume occupied by electrodes as well as the supports. The result was a mesh with 1,881,500 elements, requiring correction of 240 inverted elements. In the example wiredemonode.min, I simply replaced each cylinder with a Line of the same length. I also limited the zone of fine resolution (0.1 cm) to the region between the electrodes. The resulting mesh had 1,191,016 elements, none of which required correction. The runs times for the HiPhi solution were 624 seconds for the mesh with volumetric models and 349 seconds for the mesh with node models. The second figure below shows the distribution of potential with the 0.2 cm radius rods (top) versus the filamentary wires (bottom). The plotted values of potential in the region between the electrodes are indistinguishable. For the quantitative comparison, the values of |E| at the position shown by the red dot differed by less than 0.4% between the two solutions.
In conclusion, you can often avoid problems and reduce run time in electrostatic calculations by using node models. These models are appropriate for small or thin objects when they are not close to the region of interest. Use fitted volumetric models only when they significantly affect critical fields. For example, if we were interested in the field amplitude at the feedthrough for the 25 kV electrode, we should represent the true cylindrical shape of the support rod within and near the dielectric.