Combined Immersed Boundary Finite-Element Methods for Complex Flow Simulations

摘要

The purpose of present study aims at the combination of immersedrnboundary and finite-element methods for complex flow simulations. The modelrnbased on the Navier-Stokes equations is devised for the solution of the viscousrnflows with immersed boundaries using immersed boundary finite-element methodsrn(IBFEM). The governing equation is discretized by finite element method on arnnon-uniform Cartesian mesh using the primitive variables formulation. Numericalrnsolutions for the scenarios with three variables, two velocities and one pressure arernobtained by adopting decoupled numerical solution procedure. Geometriesrnfeaturing the flexible solid obstacles in the flow are embedded in the Cartesian gridrnwith special discretizations near the embedded cell to ensure the accuracy of thernsolution in the cut cells. A volume of solid/fluid in the cut cell is estimated tornenforce the volume conservation enclosed by an immersed boundary that allows usrnto compute the virtual forces inside the embedding bodies. The present studyrnnaturally gives more reasonable results on problems including the flow past arncircular cylinder, flow past two circular cylinders of different diameters. The timernhistory of drag and lift coefficients also should be implemented. Moreover, therntime-based variation of the flow phenomena such as vorticity field is sketched inrnthis study. Thus, it is convinced that the combined immersed boundary finite elementrnmethods are robustness and accuracy of solving viscous fluid flow.