Study Of A Discrete Forcing Finite-volume Immersed Boundary Method

Moving boundary flow problems,such as fish swimming,birds flying,blood flow in human heart valve,and weapon delivery of military aircraft,etc.are demanding and difficult to tackle in the area of fluid mechanics.Immersed boundary(IB)methods have been attracting more and more attention in recent years because of their ability to simulate moving boundary problems on fixed meshes.This thesis focuses on a discrete forcing finite-volume IB method which encloses the finite volume discretization of the governing equations at the near-wall nodes by some approximate form of the solution near the immersed boundary.Based on the different location of the "forcing points",this IB method can be classified into local DFD method and finite-volume HCIB method."Forcing points"in local DFD refer to the mesh nodes in the immediate vicinity of the boundary outside the solution domain,whereas in finite-volume HCIB they refer to the mesh nodes in the immediate vicinity of the boundary inside the solution domain.The content of this thesis consists of the following aspects:(1)A finite volume HCIB method for incompressible Navier-Stokes equations is proposed.Galerkin finite volume approximation is employed for spatial discretization.The flow-variables at an immersed boundary point are evaluated via an approximation of quadratic polynomial in normal direction to wall,which is associated with no-slip boundary condition and the simplified local momentum equation.The present method is also extended to solve three-dimensional geometrically complex moving-boundary problems.Compared to the original finite difference HCIB method,the present method is not only suitable for Cartesian meshes,but also for unstructured meshes.Moreover,the "multi-valued points"problem for thin bodies in local DFD can be avoided in the present method,thus makes it much easier to implement.(2)A finite volume HCIB method for simulating inviscid compressible flows governed by Euler equations is proposed.Galerkin finite volume approximation is also employed for spatial discretization.The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary.The normal velocity is evaluated by applying the no-penetration boundary condition,and therefore the influence of solid wall in the inviscid flow is taken into account.The pressure is computed with the local simplified momentum equation,and the density and the tangential velocity are evaluated by using the constant-entropy relation and the constant-total-enthalpy relation respectively.With a local coordinate system,the present method has been extended easily to the three dimensional case.Compared with the ghost-cell method orthe DFD method,the tedious task of handling multi-valued points can be eliminated in the present method.There is no need to regenerate various irregular cells to achieve the boundary-conformity as performed in the cut-cell methods.(3)For the local DFD method,two approaches are proposed to reduce spurious oscillations in the simulation of moving-boundary problems,i.e.,the hybrid reconstruction approach and mass source/sink treatment.For the hybrid solution reconstruction approach,the reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary,which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall.Therefore,the reconstructed solution can account for the smooth movement of the immersed boundary.By introducing a mass source/sink term into the continuity equation,the mass-conservation property of the local domain-free discretization(DFD)method is improved to reduce the spurious oscillations in the simulation of moving-boundary problems.The mass source/sink term is constructed by evaluating the mass flux through the solid part of control volume split by the immersed boundary.It is shown that both approaches can effectively reduce the numerical oscillations with little additional computational cost,and the spatial accuracy of the original local DFD method can also be preserved.(4)A partitioned strong coupling approach is developed to simulate fluid-structure interaction(FSI)of both rigid and flexible bodies,and the stability and convergence of this approach are analyzed.A predictor-corrector approach is developed to accelerate convergence and reduce cost of the implicit coupling.Specifically,physics-based predictors with lower computational cost are used in place of full flow and solid solvers to perform FSI iterations,while the full solvers are only used for the correction step.The general framework of this coupling approach is flexible so that it is not limited to the individual flow and solid solvers used in the current study and can be applied to couple many existing packages.We have applied this coupling approach to both rigid and elastic bodies to demonstrate its accuracy and efficiency.Extensive numerical experiments for flows involving two/three dimensional,fixed/moving,rigid/flexible objects verify the accuracy and efficiency of the various proposed and developed numerical methods.