Overset Adaptive Cartesian/Prism Grid Method for Stationary and Moving-Boundary Flow Problems

Abstract

T HE use of unstructured grids in computational fluid dynamics (CFD) has become widespread during the last two decades, due to their ability to discretize arbitrarily complex geometries and the flexibility in supporting solution-based grid adaptations to enhance the solution accuracy and efficiency [1–7]. In the early days of unstructured grid development, triangular/tetrahedral grids were employed the most in dealing with complex geometries. Recently, mixed or hybrid grids including many different cell types have gained popularity because of the improved efficiency and accuracy over pure tetrahedral grids. For example, hybrid prism/tetrahedral grids [8], mixed grids including tetrahedral/prism/pyramid/ hexahedral cells [9], and adaptive Cartesian grid methods [10–15] have been used in many applications with complex configurations. The success demonstrated by unstructured grids for steady flow problems has prompted their applications to unsteady, movingboundary, flow problems. A powerful approach for moving-boundary flow problems is the overset Chimera grid method [16]. Originally, the Chimera grid method was used to simplify domain decomposition for complex geometries using structured grids. The method is particularly useful for moving-boundary flow simulations because grid remeshing can be avoided [17]. However, frequent hole-cutting and donor-cell searching may be necessary to facilitate communications between the moving Chimera grids. With continuous improvement over the last decade and a half, the Chimera grid method has achieved tremendous success in handling very complex moving-boundary flow problems.More recently, to further simplify the grid-generation process, unstructured grids are also used in aChimera grid system for moving-boundary flow computations, making the approach even more flexible in handling complex geometries [18]. In this Technical Note, we advocate the use of an overset adaptive Cartesian/prism grid method for moving-boundary flow computations. Themethod combines the advantage of the adaptive Cartesian/ prism grid in geometry flexibility with that of the Chimera approach in tacklingmoving-boundary flowwithout grid remeshing. There are several reasons why an adaptive Cartesian grid is used for movingboundary problems: 1) Cartesian cells are more efficient at filling space given a certain length scale than triangular/tetrahedral cells. 2) Searching operations can be performed very efficiently with the octree data structure. 3) Solution-based and geometry-based grid adaptations are straightforward to carry out. The grid-generation process is as follows. Body-fitted prism grids are generated first near solid bodies to resolve viscous boundary layers using the advancing layer approach by marching the prism-layer grid in the approximate surface normal directions. The prism-grid-generation approaches (and their limitations) have been well researched in the literature in the past two decades, for example, in [6,8,18,19], and the current implementation follows similar ideas. Therefore, interested readers should consult these references for prism-grid-generation methods and their limitations. An adaptive Cartesian grid is then generated to cover the outer domain and serve as the background grid for bridging the “gaps” between the prism grids. The outer boundaries of the prism grids are used to generate holes in the adaptive Cartesian grid to facilitate data communication. If the bodies move, the prism grids move with the bodies, whereas the Cartesian grid remains stationary. After a few (tens of) time steps, new holes are cut out of the Cartesian grids, and new donor cells are also identified. Solution fields are interpolated from the old Cartesian grid to the new grid using a cellwise linear reconstruction technique. This Technical Note is organized as follows. In the next section, the overset adaptive Cartesian/prism grid-generation and holecutting approaches will be presented, together with illustrative examples. In Sec. III, several steady and unsteady moving-boundary flow problems are computed. Grid-refinement studies are performed to ensure the computational solutions are grid-independent. Computational results are compared with experimental data and other simulations whenever possible. Finally, conclusions from this study are summarized in Sec. IV.