Mesh adaptation through r-refinement using a truss network analogy

Abstract

This project investigates the use of a truss network, a structural mechanics model, as a metaphor for adapting a computational fluid dynamics (CFD) mesh. The objective of such adaptation is to increase computational effi- ciency by reducing the numerical error. To drive the adaptation, or to give the scheme an understanding of accuracy, computational errors are translated into forces at mesh vertices via a so-called monitor function. The ball-vertex truss network method is employed as it offers robustness and is applicable to problems in both two and three dimensions. In support of establishing a state-of-the-art adaptive meshing tool, boundary vertices are allowed to slide along geometric boundaries in an automated manner. This is achieved via feature identification followed by the construction of 3rd order bezier surface patches over boundary faces. To investigate the ability of the scheme, three numerical test cases were investigated. The first comprised an analytical case, with the aim of qualitatively assessing the ability to cluster vertices according to gradient. The developed scheme proved successful in doing this. Next, compressible transonic flow cases were considered in 2D and 3D. In both cases, the computed coefficient of lift and moment were investigated on the unrefined and refined meshes and then compared for error reduction. Improvements in accuracy of at least 60% were guaranteed, even on coarse meshes. This is viewed as a marked achievement in the sphere of robust and industrially viable r-refinement schemes.