An adaptive least-squares method for the compressible Euler equations

• Published in: International journal for numerical methods in fluids 1999-12, Vol.31 (7), p.1121-1139
• Main Authors: Taghaddosi, F., Habashi, W.G., Guèvremont, G., Ait-Ali-Yahia, D.
• Format: Article
• Language: English
• Subjects: artificial viscosity; Compressible flows; shock and detonation phenomena; Computational methods in fluid dynamics; Euler equations; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); grid adaption; least-squares method; Physics; Shock-wave interactions and shock effects; Shock-wave interactions and shockeffects; Transonic flows
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19991215)31:7<1121::AID-FLD913>3.0.CO;2-R

An adaptive least‐squares finite element method is used to solve the compressible Euler equations in two dimensions. Since the method is naturally diffusive, no explicit artificial viscosity is added to the formulation. The inherent artificial viscosity, however, is usually large and hence does not allow sharp resolution of discontinuities unless extremely fine grids are used. To remedy this, while retaining the advantages of the least‐squares method, a moving‐node grid adaptation technique is used. The outstanding feature of the adaptive method is its sensitivity to directional features like shock waves, leading to the automatic construction of adapted grids where the element edge(s) are strongly aligned with such flow phenomena. Using well‐known transonic and supersonic test cases, it has been demonstrated that by coupling the least‐squares method with a robust adaptive method shocks can be captured with high resolution despite using relatively coarse grids. Copyright © 1999 John Wiley & Sons, Ltd.