AnAdaptive Moving Mesh Method for Two-Dimensional Incompressible Viscous Flows

In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys.,170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each timestep. The Navier-Stokes equations are solved in the vorticity stream-function form bya finite-volume method in space, and the mesh-moving part is realized by solving theEuler-Lagrange equations to minimize a certain variation in conjunction with a moresophisticated monitor function. A conservative interpolation is used to redistributethe numerical solutions on the new meshes. This paper discusses the implementationof the periodic boundary conditions, where the physical domain is allowed to deformwith time while the computational domain remains fixed and regular throughout. Numericalresults demonstrate the accuracy and effectiveness of the proposed algorithm.

The Modified Ghost Fluid Method as Applied to Extreme Fluid-Structure Interaction in the Presence of Cavitation

In this work,the modified Ghost Fluid Method is further developed to ap-ply to compressible fluid coupled to deformable structure,where the pressure in the structure or flow can vary from an initial extremely high magnitude(such that the solid medium can be under plastic compression)to a subsequently very low quantity(so that cavitation can occur in the fluid).New techniques are also developed in the definition of the ghost fluid status when the structure is under plastic deformation or when the flow is under cavitation next to the structure.Numerical results show that the improved MGFM for treatment of the fluid-deformable structure coupling works efficiently for all pressure ranges and is capable of simulating cavitation evolution and cavitation re-loading in conjunction with the employment of the isentropic one-fluid cavitation model.

Simulation of Wave-Flow-Cavitation Interaction Using a Compressible Homogenous Flow Method

A numerical method based on a homogeneous single-phase flow model is presented to simulate the interaction between pressure wave and flow cavitation.To account for compressibility effects of liquid water,cavitating flow is assumed to be compressible and governed by time-dependent Euler equations with proper equation of state(EOS).The isentropic one-fluid formulation is employed to model the cavitation inception and evolution,while pure liquid phase is modeled by Tait equation of state.Because of large stiffness of Tait EOS and great variation of sound speed in flow field,some of conventional compressible gasdynamics solvers are unstable and even not applicable when extended to calculation of flow cavitation.To overcome the difficulties,a Godunov-type,cell-centered finite volume method is generalized to numerically integrate the governing equations on triangular mesh.The boundary is treated specially to ensure stability of the approach.The method proves to be stable,robust,accurate,time-efficient and oscillation-free.Novel numerical experiments are designed to investigate unsteady dynamics of the cavitating flow impacted by pressure wave,which is of great interest in engineering applications but has not been studied systematically so far.Numerical simulation indicates that cavity over cylinder can be induced to collapse if the object is accelerated suddenly and extremely high pressure pulse results almost instantaneously.This,however,may be avoided by changing the traveling speed smoothly.The accompanying huge pressure increasemay damage underwater devices.However,cavity formed at relatively high upstream speed may be less distorted or affected by shock wave and can recover fully from the initial deformation.It is observed that the cavitating flow starting from a higher freestream velocity is more stable and more resilient with respect to perturbation than the flow with lower background speed.These findings may shed some light on how to control cavitation development to avoid possible damage to operating devices.

Flow field generated by a dielectric barrier discharge plasma actuator in quiescent air at initiation stage

A single Dielectric Barrier Discharge(DBD) plasma actuator driven by Alternating Current(AC) power, capable of inducing a starting vortex and a wall jet in quiescent air, is suited for low-Reynolds-number flow control. However, the starting vortex and the wall jet are usually observed after the plasma actuator has been operated for dozens of and hundreds of cycles of the voltage, respectively. The detail of the induced flow field at the initiation stage of the plasma actuator has rarely been addressed. At the initiation stage, a thin jet that provides the impetus for the entrainment of the induced flow at the beginning of the plasma actuation is first observed by using a high-accuracy phase-lock Schlieren technique and a high-speed Particle Image Velocimetry(PIV) system. This is the initial form of the momentum transfer from the plasma to the fluid.Then, an arched type jet is created by the plasma actuator. In addition, the whole development process of the induced flow field from the starting point of the thin jet to the quasi-steady stage of wall jet is presented for providing a comprehensive understanding of the plasma actuator and proposing a relevant enhancement of the numerical simulation model.

An Implementation ofMAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows

Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.

An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains

An indirect-forcing immersed boundary method for solving the incompressible Navier-Stokes equations involving the interfaces and irregular domains is developed.The rigid boundaries and interfaces are represented by a number of Lagrangian control points.Stationary rigid boundaries are embedded in the Cartesian grid and singular forces at the rigid boundaries are applied to impose the prescribed velocity conditions.The singular forces at the interfaces and the rigid boundaries are then distributed to the nearby Cartesian grid points using the immersed boundary method.In the present work,the singular forces at the rigid boundaries are computed implicitly by solving a small system of equations at each time step to ensure that the prescribed velocity condition at the rigid boundary is satisfied exactly.For deformable interfaces,the forces that the interface exerts on the fluid are computed from the configuration of the elastic interface and are applied to the fluid.The Navier-Stokes equations are discretized using finite difference method on a staggered uniform Cartesian grid by a second order accurate projection method.The ability of the method to simulate viscous flows with interfaces on irregular domains is demonstrated by applying to the rotational flow problem,the relaxation of an elastic membrane and flow in a constriction with an immersed elastic membrane.

Numerical Investigation of Cavitation Interacting with Pressure Wave

A computational fluid dynamics solver based on homogeneous cavitation model is employed to compute the two-phase cavitating flow.The model treats the two-phase regime as the homogeneous mixture of liquid and vapour which are locally assumed to be under both kinetic and thermodynamic equilibrium.As our focus is on pressure wave formation,propagation and its impact on cavitation bubble,the compressibility effects of liquid water have to be accounted for and hence the flow is considered to be compressible.The cavitating flow disturbed by the introduced pressure wave is simulated to investigate the unsteady features of cavitation due to the external perturbations.It is observed that the cavity becomes unstable,locally experiencing deformation or collapse,which depends on the shock wave intensity and freestream flow speed.

An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids

In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow.The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES method.In this work,the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation.The forces at the interface are calculated from the configuration of the interface and the computed augmented variable,and then applied to the fluid through the related jump conditions.The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method.The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow.Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously.These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

A BEM/FEM Coupling Approach for Fluid-Structure Interaction Simulation of Cell Motion

In this paper, accurate and efficient simulation of cell motion in a biological fluid flow is investigated. The membrane of a moving cell is represented by athin shell composed of incompressible neo-Hookean elastic materials and the liquidsaround the membrane are approximated as incompressible Newtonian flows with lowReynolds numbers. The biofluid mechanics is approximated by the Stokes flow equations. A low-order BEM model is developed for the two biological fluids coupled atthe membrane surface. The moving boundary problem in fluid mechanics can be effectively solved using the BEM with a GMRES solver. The FEM model based on a flatthin shell element is further developed to predict the membrane load due to the largedeformation of a moving cell. Computational efficiency is greatly improved due tothe one-dimensional reduction in the present BEM and FEM models. The BEM solverfor the biological fluids is coupled with the FEM solver for the cell membrane at themembrane surface. The position of the membrane surface nodes is advanced in time byusing the classical fourth-order Runge-Kutta method. Numerical instability is avoidedby using a relatively small time step. Further numerical instabilities in the FEM solveris alleviated by using various techniques. The present method is applied to the FSIproblems of cell motion in a cylindrical flow. Numerical examples can illustrate thedistinct accuracy, efficiency and robustness of the present method. Furthermore, theimportance of bending stiffness of a cell membrane for stable cell motion simulation isemphasized. It is suggested that the present approach be an appealing alternative forsimulating the fluid-structure interaction of moving cells.