An adaptive least-squares method for the compressible Euler equations

An adaptive least-squares finite element method is used to solve the compre ssible Euler equations in two dimensions. Since the method is naturally dif fusive, no explicit artificial viscosity is added to the formulation. The i nherent artificial viscosity, however, is usually large and hence does not allow sharp resolution of discontinuities unless extremely fine grids are u sed. To remedy this, while retaining the advantages of the least-squares me thod, a moving-node grid adaptation technique is used. The outstanding feat ure of the adaptive method is its sensitivity to directional features like shock waves, leading to the automatic construction of adapted grids where t he element edge(s) are strongly aligned with such flow phenomena. Using wel l-known transonic and supersonic test cases, it has been demonstrated that by coupling the least-squares method with a robust adaptive method shocks c an be captured with high resolution despite using relatively coarse grids. Copyright (C) 1999 John Wiley & Sons, Ltd.