Adaptive mesh generation for fluid mechanics problems

In this study, we give an in depth investigation of the adaptive procedures for compressible and incompressible flow problems. Many tests have been carried out with different error indicators for different problems. These refinement procedures show that the interpolation error indicators are adequate to predict an accurate solution. Comparison between the gradient and curvature-based error indicators show that the former yields better performance in most situations. However, we found that the latter indicators predict better motion in the recirculatory and unstable regions, than the gradient-based method. Many test cases have been presented for both compressible and incompressible flow problems. In the later part of the paper, we suggest a simple way of combining the curvature/gradient indicators of different key variables and present an appropriate problem where it is applicable. A wide coverage of relevant literature has also been presented in this paper.