Evaluation of geometric conservation law using pressure-based fluid solver and moving grid technique

The geometric conservation law (GCL) is an important concept for moving grid techniques because it directly regulates the treatments of the fluid flow and grid movement. With the grid movement at every time instant, the Jacobian, associated with the volume of each element in curvilinear co-ordinates, needs to be updated in a conservative manner. In this study, alternative GCL schemes for evaluating the Jacobian have been investigated in the context of a pressure-based Navier-Stokes solver, utilizing moving grid and the first-order implicit time stepping procedure as well as the PISO scheme. GCL-based on first and second-order, implicit as well as time-averaged, time integration schemes were considered. Accuracy and conservative properties were tested on steady-state, laminar flow inside a 2D channel and time dependent, turbulent flow around a 3D elastic wing; both treated with moving grid techniques. It seems that the formal order of accuracy is not a decisive indicator. Instead, the speed of grid movement and the interplay between the flow solver and the GCL treatments make a more noticeable impact