INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2001; 51:1053–1077 A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two-dimensional laminar ows in external ow elds D. L. Young *;† , J. T. Chang and T. I. Eldho Department of Civil Engineering and Hydrotech Research Institute; National Taiwan University; Taipei; 10617; Taiwan SUMMARY This paper describes a new computational model developed to solve two-dimensional incompressible viscous ow problems in external ow elds. The model based on the Navier–Stokes equations in primitive variables is able to solve the innite boundary value problems by extracting the boundary eects on a specied nite computational domain, using the pressure projection method. The external ow eld is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the innite boundary. The momentum equation of the ow motion is solved using the three-step nite element method. The arbitrary Lagrangian–Eulerian method is incorpo- rated into the model, to solve the moving boundary problems. The present model is applied to simulate various external ow problems like ow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still uid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright ? 2001 John Wiley & Sons, Ltd. KEY WORDS: Navier–Stokes equations; external ow; arbitrary Lagrangian–Eulerian method; boundary elements; nite elements 1. INTRODUCTION The two-dimensional laminar viscous ow problems in external ow elds have been the focus of numerous investigations. These studies have been motivated by the desire to under- stand the fundamental physics of such ows as well as their practical importance in various industries. The phenomena of external ow problems are visible everywhere around our living environments such as: the variation of ow eld arisen by the wind across the high- rise building, the drag force induced by driving car accelerating in the wind and also the * Correspondence to: Der-Liang Young, Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, 10617, Taiwan. † E-mail: dlyoung@hy.ntu.edu.tw Contract=grant sponsor: National Science Council of Taiwan Received 6 December 1999 Copyright ? 2001 John Wiley & Sons, Ltd. Revised 9 October 2000