WorkshopsPressure correction methods for creeping flows using the axial Green’s function formulation
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We propose a projection method of the velocity field onto the divergence free space using the axial Green’s function method (AGM). The key difficulty of the AGM to creeping flow problem is laid on the fact that it is governed by a system of equations, the momentum equations and the continuity equation. The resultant formulation for the flow consists of one-dimensional integral equations on axial lines associated with arbitrary cross point. The equation induced from the divergence free condition explicitly reveals the pressure variable. It results in stable pressure correction algorithms. While FEM or FDM uses two approximation spaces (LBB-elements or Staggered grids) for the velocity and pressure for the purpose of stability, the AGM for incompressible flows uses the same nodes for the velocity and the pressure. Discretizing the integral equations, we finally obtain a system of linear equations for the newly introduced variables which result from splitting the partial differential operators. The numerical solution preserves the second order convergence rate for the velocity and the first order for the pressure.
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Do Wan Kim
2012-02-17
09:50:00 - 10:30:00
R101 , Astronomy and Mathematics Building
We propose a projection method of the velocity field onto the divergence free space using the axial Green’s function method (AGM). The key difficulty of the AGM to creeping flow problem is laid on the fact that it is governed by a system of equations, the momentum equations and the continuity equation. The resultant formulation for the flow consists of one-dimensional integral equations on axial lines associated with arbitrary cross point. The equation induced from the divergence free condition explicitly reveals the pressure variable. It results in stable pressure correction algorithms. While FEM or FDM uses two approximation spaces (LBB-elements or Staggered grids) for the velocity and pressure for the purpose of stability, the AGM for incompressible flows uses the same nodes for the velocity and the pressure. Discretizing the integral equations, we finally obtain a system of linear equations for the newly introduced variables which result from splitting the partial differential operators. The numerical solution preserves the second order convergence rate for the velocity and the first order for the pressure.
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