An adaptive finite element method for planar and axisymmetric compressible flows

Numerical simulation results for the least squares finite element method (LSFEM) are presented for a purely hyperbolic model describing the two-dimensional planar and axisymmetric compressible flows. The LSFEM is combined with a grid adaptation technique based on the well-known spring analogy system enhanced by a grid smoothening technique. Such technique has been applied to prevent abrupt changes in the element angles so as to maintain the global stiffness matrix well posed. The time stepping effect on the steady-state solution is investigated. This method proved to be more accurate compared to some existing techniques despite using fewer nodes.