A simulation technique for 2-D unsteady inviscid flows around arbitrarily moving and deforming bodies of arbitrary geometry

Abstract

A new technique for the time-accurate numerical simulation of Euler flows around moving and deforming bodies in 2-D is presented. The grid used is of the stationary, Cartesian, unstructured, Quadtree-based type. The use of a stationary grid is made possible by allowing bodies to move across grid-lines. Use is made of the property that the cells in the immediate vicinity of a moving or stationary body can always be merged together to form combined cells that are topologically invariant over a motion step. Without degrading the global order of accuracy, this merging eliminates the CFL number constraint imposed by cut cells of small area, and eliminates the need for special handling of cells that, due to the motion of bodies across grid-lines, are uncovered or swept-over. The flow solver used is based on a finite-volume conservative formulation, and Roe's approximate-Riemann-solver is used for the computation of interface fluxes. 1-exact spatial reconstruction is used in conjunction with a predictor-corrector explicit timemarching scheme to obtain spatial and temporal second-order accuracies. Gradient limiting is used to enforce monotonicitypreservation near discontinuit,ies. In order to resolve flow features economically and controllably the grid is adaptable to both the geometry and and the flow solution. The computational resources required by this technique are shown to be typical of unstructured-grid implementations. Two computations are presented to demonstrate the capabilities and validity of the technique.