Mesh Adaptation Based On Projection And Wake Of Error For Simulation Of Unsteady Flows

In this paper, we propose a mesh adaptation technique based on error projection and error wake for simulation of unsteady flows. For each period of mesh adaptation, adaptation indicators are projected ahead of their current location over a given distance, ensuring that flow features propagate into a refined region. It is determined by the error wake when the current adaptation period stops and the next one starts(regenerate the adaptive mesh). In each adaptation period, the mesh is refined where the features are traversing and unrefined where they deviated. The adaptation indicator is defined by using the physical quantities in the flow field, such as the magnitude of vorticity or pressure gradient. There is no lag between the adapted mesh and the computed solution, and the adaptation frequency can be controlled. Therefore, the errors due to the solution transferring can be reduced. To ensure the conservation property of solution, we use a conservative linear interpolation for the unstructured grids to transfer the numerical solution from the old mesh to the new adapted one.Compared with the previous methods, there is no need to predict the flow field, the flow equations are only solved one time, and the efficiency of mesh adaptation is raised. The flow equations are solved by local DFD(Domain-Free-Discretization) method. This method can simulate the flow with moving boundaries on a fixed mesh. In order to verify the present mesh adaptation method, we simulate the movement of vortex in the free stream and unsteady flows around a single cylinder, double cylinders and an oscillating NACA0012 airfoil. The results of numerical experiments show that the present method can improve the accuracy and efficiency of the mesh-adaptive simulation of unsteady flows.