Ghost Cell And Gradient-augmented Level Set Methods Based Fluid Structure Interaction Algorithm And Its Applications

Free surface flows interacting with rigid or flexible bodies are common in many ocean engineering applications such as wave impact,liquid sloshing and vortex induced vibration.It involves complex coupling features,including complex multiple bodies,nonlinear free surface,large deformation of structures et al..The accurate simulation of these flow phenomena is very important and fairly challenging.To simulate complex multibody,3D(Three Dimensional)free surface,large deformation FSI(Fluid Structure Interaction)problems,many existed literatures are based on the commercial CFD/CSD(Computational Fluid Dynamics/ Computational Solid Dynamics)software.Rare literatures involves house-developed FSI codes.In this paper,a Cartesian grid based multiphase FSI computational method and Corresponding codes in Fortran 90 are developed to simulate rigid or flexible structures interacting with free surface flows.The main contents are as follows:The N-S equations governing the incompressible viscous flows and the discretization method are described.a time semi-implicit finite difference method is used to solve incompressible N-S equations on a fixed staggered Cartesian grid.For time integration,a fractional step method combined with a TVD-RK3(Total Variation Diminishing-Third Order Runge-Kutta)scheme is used.For spatial discretization,convective fluxes are handled by a Roe's flux difference splitting method with a higher-order TVD-MUSCL(Total Variation Diminishing Monotonic Upstream-centered Scheme for Conservation Laws)scheme.An ICCG(Incomplete Cholesky Conjugate Gradient)method is coupled with a diagonal storage format to solve the large sparse symmetric positive definite matrix.The Taylor-Green flow is simulated to validate the accuracy of the present N-S solver.The present N-S solver can obtain second-order accuracy in space and first-order accuracy in time.To treat arbitrary rigid or flexible moving boundaries in the fluid,a radial basis function ghost cell method is developed.In this method,the RBF(Radial Basis Function)is introduced to fit the arbitrary body surface with a finite number of offset points.Therefore,the phase state of the grid cell can be easily identified by the signed iso-surface function.A RBF interpolation scheme is constructed to interpolate ghost cell variables,to enforce boundary conditions on complex surfaces.For violent pressure oscillations of moving boundaries in the Cartesian grid method,a FAR(Fractional Area Representation)method is developed.The local mass conservation is improved by correcting the Possion equation for pressure,thus reducing the violent pressure oscillations.To validate the accuracy and capability of the present ghost cell method,several test cases are simulated.The cases include 3D flows around a sphere,a cube and a ellipsoid,in-line oscillation of a circular cylinder,the uniform flow around a pitching hydrofoil and the free falling of a particle.To capture highly non-linear free surface,a 3D GALS(Gradient-Augmented Level Set)two-phase flow model is devloped based on a 2D(Two Dimensional)GALS two-phase flow model.Also,a simple distance function assignment method is proposed to treat the contact boundary between the 3D free surface and the arbitrary solid surface,thus the present two-phase flow model can be extended to simulate wave structure interaction.In this GALS two-phase flow model,a generalized CIR(Courant,Isaacson,Reese)method is used to solve the level set and gradient equations simultaneously.A Hermite cubic scheme is used to interpolate level set value at arbitrary positions and a Lagrange polynomial scheme is used to interpolate velocity field and its derivatives.A modified Newton method is used to conduct node-wise reinitialization on a narrow band.To validate the accuracy and mass conservation property of the present method,liquid sloshing in a horizontal excited rectangular tank,wave propagation and 3D dam-break are simulated.To predict the motion and deformation response of the flexible body,an ANCF(Absolute Nodal Coordinate Formulation)based finite element code is developed.To simulate flexible boundary FSI problems,a flexible interface point reconstruction strategy is developed to transfer the field information between finite element nodes and the background grid.In this ANCF method,2D or 3D Euler and shear beam models are derived.The load increment method is combined with the Newton-Raphson iterative method is used to solve non-linear finite element equations.Large deformation of a cantilever beam and the free falling of a very flexible pendulum are simulated.the ANCF method is validated to be capable of predicting large deformation,large displacement of flexible structures.The proposed distance function assignment method is used to combine the ghost cell method and the GALS method to simulate the 3D wave-structure interaction.Non-linear sloshing under combined surge and sway excitations in a 3D rectangular tank is simulated.The accuracy of the present method is validated when the present results are compared with numerical and analytic results.Further,parametric studies on the excitation frequency and baffle height are conducted.Then,liquid sloshing under rotational excitation in a 3D prismatic tank is simulated.Good agreements between the present results and experimental data are obtained.Also,the effects of water depth on the free surface elevation and the slamming load are studied.The proposed interface point redistribution strategy is used to combine the ghost cell method and the ANCF method to simulate the flexible body interacting with the fluid.Uniform flows around one oscillating hydrofoil under different excitation frequencies are simulated.The accuracy and reliability of the present method are validated by comparing with previous numerical results.Further,the swimming mechanism of fish is clarified.Also,flows around two oscillating hydrofoils are simulated,and the effects of the excitation frequency and the gap distance on the flow patterns and force coefficients are studied.Then,flow induced oscillation responses of one flapping filament and two parallel flapping filaments in an incoming flow are simulated.The accuracy and reliability of the present method are validated.Sensitivity analysis on the material parameter is conducted,and the flapping characteristics are analyzed.