Computation Of 2d Inviscid Compressible Flow Using An Entropy Consistent Euler Flux - Roslan, Nur Khairunnisa Hanisah (2013)
The Roe flux function is one of the most established flux functions for inviscid flow and widely used in many CFD codes. However, the Roe flux suffers from shock instability which is usually observed for very strong shocks as in hypersonic flow. This maybe because the Roe flux does not strictly adhere to the second law of thermodynamics which is critical to capture shocks. The entropy consistent Euler flux (EC) is a new shock capturing method developed by Ismail & Roe in an attempt to overcome the above mentioned deficiencies of the Roe flux. The EC flux is designed to discretely satisfy the basic conservation laws, besides satisfying the second law of thermodynamics (entropy control). Most of the previous studies on the entropy schemes are based mainly on academic test problems using one-dimension. The main objective of this study is to determine the performance of the EC flux function relative to the Roe flux under subsonic, transonic, supersonic and hypersonic flow. This new flux function is tested for 1D and 2D test problems. The 1D test problem is based on Sod’s shock tube problem, whereas the 2D problems include the Mach 3 flow over a staircase, a steady flow over a cylinder and a steady flow over a NACA 0012 airfoil. In order to solve these 1D and 2D problems, an in-house CFD research code based on inviscid compressible flow was developed for a general 2D curvilinear geometry using structured grids. The grid is generated using GAMBIT software and then fed into a self-written converter software to ensure that the grid configurations are compatible with the newly developed CFD solver.