Mesh adaptation for simulation of unsteady flow with moving immersed boundaries

Abstract

SUMMARYIn this work, an approach for performing mesh adaptation in the numerical simulation of two‐dimensional unsteady flow with moving immersed boundaries is presented. In each adaptation period, the mesh is refined in the regions where the solution evolves or the moving bodies pass and is unrefined in the regions where the phenomena or the bodies deviate. The flow field and the fluid–solid interface are recomputed on the adapted mesh. The adaptation indicator is defined according to the magnitude of the vorticity in the flow field. There is no lag between the adapted mesh and the computed solution, and the adaptation frequency can be controlled to reduce the errors due to the solution transferring between the old mesh and the new one. The preservation of conservation property is mandatory in long‐time scale simulations, so a P1‐conservative interpolation is used in the solution transferring. A nonboundary‐conforming method is employed to solve the flow equations. Therefore, the moving‐boundary flows can be simulated on a fixed mesh, and there is no need to update the mesh at each time step to follow the motion or the deformation of the solid boundary. To validate the present mesh adaptation method, we have simulated several unsteady flows over a circular cylinder stationary or with forced oscillation, a single self‐propelled swimming fish, and two fish swimming in the same or different directions. Copyright © 2012 John Wiley & Sons, Ltd.

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

“…For a long‐time simulation, these errors may accumulate. In order to solve this problem, the prediction‐correction scheme proposed by Zhou and Ai for 2‐dimensional problems is implemented in the present 3‐dimensional framework.…”

“…Mesh adaptation methods can be categorized roughly into mesh deformation (r‐refinement), re‐meshing, and element division (h‐refinement) . Mesh deformation method can maintain the mesh topology, but it is not suitable for situations where the motion or deformation of the object is arbitrary.…”

“…By merging the 8 subcells obtained by regular refinement, the mesh is coarsened. The strategy of dynamic mesh adaptation for time‐dependent problems proposed by Zhou and Ai is implemented in the 3‐dimensional framework. Since the used mesh is not required to coincide with the solid boundary, no special attention is paid to the curved boundary when adjusting the mesh.…”

“…This method can eliminate the lag between mesh and unsteady solution, but the inner iteration is time consuming. Zhou and Ai proposed an approach of dynamic mesh adaptation for the numerical simulation of 2‐dimensional unsteady moving‐boundary flows, in which a prediction‐correction scheme is employed to capture the evolving physical phenomena and eliminate the time shift between mesh and solution.…”

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

“…The performance of present IB method for moving‐boundary problems is tested by calculating the transonic flow over an oscillating NACA0012 airfoil. In order to reduce the computational cost, the approach of dynamic mesh adaptation proposed in the work of Zhou and Ai is employed in this work. To capture the shock waves and the boundary layers, the criterion of mesh adaptation is based on the vorticity and the density gradient in the flow field.…”