Abstract
Nonuniform mesh is beneficial to reduce computational cost and improve the resolution of the interest area. In the paper, a cell-based adaptive mesh refinement (AMR) method was developed for bearing cavitation simulation. The bearing mesh can be optimized by local refinement and coarsening, allowing for a reasonable solution with special purpose. The AMR algorithm was constructed based on a quadtree data structure with a Z-order filling curve managing cells. The hybrids of interpolation schemes on hanging nodes were applied. A cell matching method was used to handle periodic boundary conditions. The difference schemes at the nonuniform mesh for the universal Reynolds equation were derived. Ausas’ cavitation algorithm was integrated into the AMR algorithm. The Richardson extrapolation method was employed as an a posteriori error estimation to guide the areas where they need to be refined. The cases of a journal bearing and a thrust bearing were studied. The results showed that the AMR method provided nearly the same accuracy results compared with the uniform mesh, while the number of mesh was reduced to 50–60% of the number of the uniform mesh. The computational efficiency was effectively improved. The AMR method is suggested to be a potential tool for bearing cavitation simulation.
Highlights
(2) Due to the complexity of the adaptive mesh refinement (AMR) method, the basic AMR algorithm was in the paper
It can be seen that the refined meshes tagged by the pressure-based error estimation were basically distributed in the region with large pressure gradients, and the refined meshes tagged by density ratio-based error estimation were basically distributed in the region of cavitation interfaces where the density ratio gradients were large
Reynolds equation was numerically solved on the nonuniform
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The main issue that existed in the Elrod algorithm was the occasional instability that occurs during the abrupt change of switch functions. It sometimes limited the application in practical cavitation problems. A regularized cavitation algorithm developed by Nitzschke et al [17] was applicative due to the same idea of employing smooth switch functions Another way to overcome the instability was to use the non-switch function algorithm proposed by Ausas et al [18,19]. To further improve the computational efficiency, the paper employed the adaptive mesh refinement (AMR) method in the bearing cavitation simulation.
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