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Three Dimensional Incompressible Unsteady Flow in a Circular Tube with Strong Curvature Using the Navier-Stokes Equations

Author(s): Kidoo Park; Kil Seong Lee; Won Gu Kang

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Keywords: Cardiovascular Fluid Mechanics; Incompressible Navier-Stokes Equations; Generalized Curvilinear Coordinates; Artificial Compressibility Method; Quadratic Upstream Interpolation for Convective Kinematics Scheme; Artificial Dissipation; Runge-Kutta Time-Ste

Abstract: A numerical method has developed to simulate the various unsteady problems such as t he simulations of river hydraulics including natural river channels with complex hydraulic structures such as bridge piers, abutments, and complexity of flow in a meandering channel and cardiovascular fluid mechanics. The governing equations in generalized curvilinear coordinates for 3D laminar flow are the Incompressible Navier-Stokes (INS) equations and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. The time derivative terms are discretized with second order accurate, three-point backward, temporal integration scheme. The convective terms are employed using the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme. However, central differencing for the pressure gradients is discretized by adding the third-order, fourth-difference artificial dissipation method to eliminate the odd-even decoupling of the pressure field due to the non-staggered grid system. This method adopts a dual time-stepping Artificial Compressibility (AC) method integrated in pseudo-time until the pseudo-time derivative is reduced to a small tolerance and the time accurate Navier-Stokes (NS) equations. This computational implementation is a four-stage, explicit, Runge-Kutta time-stepping procedure to integrate the discrete system of governing equations in time under the multigrid methods. To evaluate this numerical ability of the method to simulate flows, we apply it to compute pulsatile flow in a circular tube with strong curvature. This algorithm yields identical velocity profiles that are in good overall agreement with an experimental measurement (Rindt&Steenhoven, 1991) for a circular tube with 90°bend except the deceleration phase of the pulsation cycle.


Year: 2010

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