An Adaptive Unstructured Mesh Method for Transient Flows Involving Moving Boundaries

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Department of Civil Engineering, University of Wales, Swansea SA2 8PP, United Kingdom
O.Hassan@swansea.ac.uk

Abstract
Introduction

Unstructured mesh methods are now widely employed for the simulation of steady 3D aerodynamic flows involving complex geometrical configurations. The attractive features of the approach are the ease with which domains of arbitrary geometrical shape can be meshed and the ability to incorporate mesh adaptivity in a natural and straightforward manner. As confidence in the approach increases, researchers are beginning to turn their attention to the possibility of extending its range of application. In this paper, we will consider one such extension to the simulation of transient inviscid compressible flows with moving boundary components.

The Approach

The spatial domain is discretised into a mesh of linear tetrahedral elements, with the initial discretisation being achieved by a Delaunay approach, with automatic point creation [1]. To enhance the efficiency of the resulting computational procedure, an edge based representation of the mesh is adopted [2]. The unsteady Euler equations are spatially discretised using a Galerkin method, with stabilisation and discontinuity capturing achieved by the adoption of a numerical flux function of JST form. The solution is advanced in time by an explicit multi-stage scheme. The implementation of the resulting procedure in a manner likely to produce results within acceptable timescales is a significant challenge. Parallelisation of the approach and the use of a parallel computing platform, such as the CRAY T3D, is one method of addressing this problem. Another promising way to achieve good speed up whilst maintaining the time accuracy is to employ a domain decomposition technique [3]. Instead of using a single timestep throughout the computational domain, it will be shown that the elements can be grouped according to the maximum allowable timestep size and be advanced independently within each group. It will be demonstrated that a high level of efficiency can be accomplished by the use of an appropriate domain decomposition procedure.

To allow for boundary movement, the mesh has to be modified as the solution progresses. Different possible methods of achieving this are considered and the approach adopted involves mesh movement with local mesh regeneration. An important feature in the success of the algorithm is to ensure local boundary recovery during the mesh regeneration. Mesh adaptation is also employed to enhance the definition of moving flow features, such as shocks.

Results

A number of different examples will be presented which demonstrate the numerical performance of the proposed approach in the transonic range, including the transient 3D inviscid simulation of the separation of a shuttle vehicle from its booster. The procedures have also been applied to the simulation of the unsteady flow over an oscillating B60 aircraft configuration, consisting of wings, pylons and powered engines. The initial mesh consists of 745 198 elements and 135 760 nodes and the starting condition is the converged steady state solution obtained in the absence of oscillation. Figure 1 shows the computed pressure contour distributions on the aircraft surface at different times during the second cycle of the computation. Tables 1 and 2 show the performance statistics achieved for the oscillating B60 using two domain decomposition methods.

(Figure and tables omitted)