Adaptive unstructured grid generation for engineering computation of aerodynamic flows

Abstract

A unified framework is presented for automatic unstructured grid generation and grid flow adaptation. The method can simultaneously refine and coarsen the grid cells, a capability that is heavily required in transient flow problems. The proposed method includes a Cartesian grid generation approach in the first stage that enables an automatic field discretization without need to explicitly define the surface grid. The Cartesian grid cells are then subdivided in such a way that prevents the existence of hanging nodes. This allows the application of efficient fully unstructured flow solvers. The capabilities of the method are demonstrated by flow computation around a maneuver wing-flap geometry (SKF 1.1) at transonic flow conditions. An explicit finite volume cell-centered scheme is used for numerical solution of compressible inviscid flow equations. Results show the efficiency and applicability of the method.

Introduction

Recent progress in computer technology has made the Computational Fluid Dynamics (CFD) methods more applicable, even at early stages of industrial design problems. One of the most important requirements of a CFD method is a short turn-around time from an initial CAD geometry to a final flow solution. Generation of an efficient computational grid usually takes significant portion of total time, as it is a skilled and time-consuming exercise. High quality mesh generation is also an important task due to its effect on accuracy and convergence of the flow solution.

Grid generation techniques can be broadly classified into structured grid generators (including boundary-fitted curvilinear co-ordinate systems [11]), unstructured grid generators (including advancing front [7] and Delaunay triangulation [13]) and hierarchical tree-based methods [3]. As the geometrical complexity of simulation domains increases, there is a growing need for generating unstructured grids. Triangulation or even mixed element discretization are much more flexible than the structured grids and can approximate complex boundaries with higher accuracy.

The use of hierarchical tree-based methods as a domain decomposition method for computer graphics and solid modeling was proposed as early as late 1970s. The use of quad trees and octrees for two- and three-dimensional finite element grid generation has been considered by Yerry and Shephard [14]. Quad trees were also used to generate adaptively refined Cartesian grids for the Euler and Navier–Stokes equations [15], [12]. Binary trees were used to generate solution-adaptive Cartesian grids for viscous and inviscid flows [2]. These have been driven by the recognition that, although the actual generation of a conventional triangular (tetrahedral in three-dimensions) grid can be highly efficient and fast there is still significant amount of expertise and human interaction necessary during the surface generation phase. This would be more crucial at early stages of industrial design as several geometries are required to be evaluated by CFD. The main advantage of Cartesian-based schemes is the opportunity to automate both the field and surface grid generation steps. However, the Cartesian technology allows hanging nodes to be present in the grid that requires special treatment while computing the boundary cell fluxes in a standard finite volume scheme. Several methods have been proposed to remove hanging nodes. Smith and Johnston [8], i.e., used the dual grid that is created by connecting the triangular cell centers to each other.

In the present work a procedure is introduced that subdivides the Cartesian cells into triangles, for removing hanging nodes, such that the boundary alignment is also satisfied.

Moreover, in many occasions an efficient flow adaptation routine is required such that both cell refinement and coarsening can be applied simultaneously. This has been achieved through the present approach using the binary tree data structure with the minimum local searches.

Details of the grid generation and flow adaptation procedures are presented in the following sections together with the computational results including comparison with experimental data.