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1.
A modified front‐tracking method was proposed for the simulation of fluid‐flexible body interactions with large deformations. A large deformable body was modeled by restructuring the body using a grid adaptation. Discontinuities in the viscosity at the fluid‐structure interface were incorporated by distributing the viscosity across the interface using an indicator function. A viscosity gradient field was created near the interface, and a smooth transition occurred between the structure and the fluid. The fluid motion was defined on the Eulerian domain and was solved using the fractional step method on a staggered Cartesian grid system. The solid motion was described by Lagrangian variables and was solved by the finite element method on an unstructured triangular mesh. The fluid motion and the structure motion were independently solved, and their interaction force was calculated using a feedback law. The interaction force was the restoring force of a stiff spring with damping, and spread from the Lagrangian coordinates to the Eulerian grid by a smoothed approximation of the Dirac delta function. In the numerical simulations, we validated the effect of the grid adaptation on the solid solver using a vibrating circular ring. The effects of the viscosity gradient field were verified by solving the deformation of a circular disk in a linear shear flow, including an elastic ring moving through a channel with constriction, deformation of a suspended catenary, and a swimming jellyfish. A comparison of the numerical results with the theoretical solutions was presented. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
In this paper, a new immersed‐boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite‐difference approach on a staggered mesh together with a fractional‐step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no‐slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed‐boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
Seokkoo Kang 《国际流体数值方法杂志》2015,78(2):76-88
An improved near‐wall modeling for large‐eddy simulation using the immersed boundary method is proposed. It is shown in this study that the existing near‐wall modeling for the immersed boundary (IB) methods that imposes the velocity boundary condition at the IB node is not sufficient to enforce a correct wall shear stress at the IB node. A new method that imposes a shear stress condition through the modification of the subgrid scale‐eddy viscosity at the IB node is proposed. In this method, the subgrid eddy viscosity at the IB node is modified such that the viscous flux at the face adjacent to the IB node correctly approximates the total shear stress. The method is applied to simulate the fully developed turbulent flows in a plane channel and a circular pipe. It is demonstrated that the new method improves the prediction of the mean velocity and turbulence stresses in comparison with the existing wall modeling based solely on the velocity boundary condition. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated. 相似文献
7.
In this paper, we study an interface transport scheme of a two‐phase flow of an incompressible viscous immiscible fluid. The problem is discretized by the characteristics method in time and finite elements method in space. The interface is captured by the level set function. Appropriate boundary conditions for the problem of mold filling are investigated, a new natural boundary condition under pressure effect for the transport equation is proposed, and an algorithm for computing the solution is presented. Finally, numerical experiments show and validate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
In this paper, we present a new method for simulating the motion of a disperse particle phase in a carrier gas through porous media. We assume a sufficiently dilute particle‐laden flow and compute, independently of the disperse phase, the steady laminar fluid velocity using the immersed boundary method. Given the velocity of the carrier gas, the equations of motion for the particles experiencing the Stokes drag force are solved to determine their trajectories. The ‘no‐slip consistent’ particle tracking algorithm avoids possible numerical filtration of very small particles due to the nonzero velocity field at the solid–fluid interface introduced by the immersed boundary method. This physically consistent tracking allows a reliable estimation of the filtration efficiency of porous filters due to inertial impaction. We illustrate and test our new approach for model porous media consisting of a structured array of aligned rectangular fibers, arranged in line and staggered. In the staggered geometry, the effect of the residual velocity at the solid–fluid interface is significant for particles with low inertia. Without adopting the developed no‐slip consistent numerical method, an artificial numerical filtration is observed, which becomes dominant for small enough particles. For both the in line and the staggered geometries, the filtration rate depends quite strongly and non monotonically on the particle inertia. This is expressed most clearly in the staggered arrangement in which a very strong increase in the filtration efficiency is observed at a well‐defined critical droplet size, corresponding to a qualitative change in the dominant particle paths in the porous medium. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
The incompressible Navier–Stokes equations are solved by an implicit pressure correction method on Cartesian meshes with local refinement. A simple and stable ghost cell method is developed to treat the boundary condition for the immersed bodies in the flow field. Multigrid methods are developed for both velocity and pressure correction to enhance the stability and convergence of the solution process. It is shown that the spatial accuracy of the method is second order in L2 norm for both velocity and pressure. Various steady and unsteady flows over a 2D circular cylinder and a 3D sphere are computed to validate the present method. The capability of the present method to treat a moving body is also demonstrated. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
10.
Consideration is given in this paper to the numerical solution of the transient two‐phase flow in rigid pipelines. The governing equations for such flows are two coupled, non‐linear, hyperbolic, partial differential equations with pressure dependent coefficients. The fluid pressure and velocity are considered as two principle dependent variables. The fluid is a homogeneous gas–liquid mixture for which the density is defined by an expression averaging the two‐component densities where a polytropic process of the gaseous phase is admitted. Instead of the void fraction, which varies with the pressure, the gas–fluid mass ratio (or the quality) is assumed to be constant, and is used in the mathematical formulation. The problem has been solved by the method of non‐linear characteristics and the finite difference conservative scheme. To verify their validity, the computed results of the two numerical techniques are compared for different values of the quality, in the case where the liquid compressibility and the pipe wall elasticity are neglected. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. 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. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
This paper presents the extension of a high‐resolution conservative scheme to the one‐dimensional one‐pressure six‐equation two‐fluid flow model. Only mixtures of water and air have been considered in this study, both fluids have been characterized using simple equations of state, namely stiffened gas for the liquid phase and perfect gas for the gas phase. The resulting scheme is explicit and first‐order accurate in space and time. A second‐order version of the scheme has also been derived using the MUSCL strategy and slope limiters. Some numerical results show the good capabilities of this type of schemes in the solution of discontinuities in two‐fluid flow problems, all of them are based on water/air numerical benchmarks widely used in the two‐phase flow literature. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
13.
Liquid plug propagation and rupture occurring in lung airways can have a detrimental effect on epithelial cells. In this study, a numerical simulation of a liquid plug in an infinite tube is conducted using an Eulerian–Lagrangian approach and the continuous interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information about the interface mesh. Results prior to the rupture are in reasonable agreement with the study of Fujioka et al. in which a Lagrangian method is used. For unity non‐dimensional pressure drop and a Laplace number of 1000, rupture time is shown to be delayed as the initial precursor film thickness increases and rupture is not expected for thicknesses larger than 0.10 of tube radius. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage. The peak values of those stresses increase as the initial precursor film thickness is reduced. After rupture, the peaks in mechanical stresses decrease in magnitude as the plug vanishes and the flow approaches a fully developed behavior. Increasing initial pressure drop is shown to linearly increase maximum variations in wall pressure and shear stress. Decreasing the pressure drop and increasing the Laplace number appear to delay rupture because it takes longer for a fluid with large inertial forces to respond to the small pressure drop. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
14.
This paper proposes a new immersed boundary (IB) method for solving fluid flow problems in the presence of rigid objects which are not represented by the mesh. Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Important benefit would be reached if we are able to solve the flow without the need of generating a mesh that fits the shape of the immersed objects. This work presents a finite element IB method using a discretization covering the entire domain of interest, including the volume occupied by immersed objects, and which produces solutions of the flow satisfying accurately the boundary conditions at the surface of immersed bodies. In other words the finite element solution represents accurately the presence of immersed bodies while the mesh does not. This is done by including additional degrees of freedom on interface cut elements which are then eliminated at element level. The boundary of immersed objects is defined using a level set function. Solutions are shown for various flow problems and the accuracy of the present approach is measured with respect to solutions obtained on body‐fitted meshes. Copyright © 2010 Crown in the right of Canada. 相似文献
15.
Yang‐Yao Niu 《国际流体数值方法杂志》2001,36(3):351-371
In this study, the advection upwinding splitting method (AUSM) is modified for the resolution of two‐phase mixtures with interfaces. The compressible two‐fluid model proposed by Saurel and Abgrall is chosen as the model equations. Dense and dilute phases are described in terms of the volume fraction and equations of state to represent multi‐phase mixtures. Test cases involving an air–water shock tube, water faucet, and dilute particulate turbulent flows through a 90° bend are used to verify the current work. It is shown that the AUSM based on flux differences (AUSMD) contains the mechanism to correctly capture the contact discontinuity and interfaces between phases. In addition, a successful application to dilute particulate turbulence flows by the AUSMD is demonstrated. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
16.
A numerical method is presented for the analysis of interactions of inviscid and compressible flows with arbitrarily shaped stationary or moving rigid solids. The fluid equations are solved on a fixed rectangular Cartesian grid by using a higher‐order finite difference method based on the fifth‐order WENO scheme. A constrained moving least‐squares sharp interface method is proposed to enforce the Neumann‐type boundary conditions on the fluid‐solid interface by using a penalty term, while the Dirichlet boundary conditions are directly enforced. The solution of the fluid flow and the solid motion equations is advanced in time by staggerly using, respectively, the third‐order Runge‐Kutta and the implicit Newmark integration schemes. The stability and the robustness of the proposed method have been demonstrated by analyzing 5 challenging problems. For these problems, the numerical results have been found to agree well with their analytical and numerical solutions available in the literature. Effects of the support domain size and values assigned to the penalty parameter on the stability and the accuracy of the present method are also discussed. 相似文献
17.
We present a compact finite differences method for the calculation of two‐dimensional viscous flows in biological fluid dynamics applications. This is achieved by using body‐forces that allow for the imposition of boundary conditions in an immersed moving boundary that does not coincide with the computational grid. The unsteady, incompressible Navier–Stokes equations are solved in a Cartesian staggered grid with fourth‐order Runge–Kutta temporal discretization and fourth‐order compact schemes for spatial discretization, used to achieve highly accurate calculations. Special attention is given to the interpolation schemes on the boundary of the immersed body. The accuracy of the immersed boundary solver is verified through grid convergence studies. Validation of the method is done by comparison with reference experimental results. In order to demonstrate the application of the method, 2D small insect hovering flight is calculated and compared with available experimental and computational results. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio‐vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco–Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
In the context of numerical simulations of multiphysics flows, accurate tracking of an interface and consistent computation of its geometric properties are crucial. In this paper, we investigate a level set technique that satisfies these requirements and ensures local third‐order accuracy on the level set function (near the interface) and first‐order accuracy on the curvature, even for long‐time computations. The method is developed in a finite differences framework on Cartesian grids. As in usual level set strategies, reinitialization steps are involved. Several reinitialization algorithms are reviewed and mixed to design an accurate and fast reinitialization procedure. When coupled with a time evolution of the interface, the reinitialization procedure is performed only when there are too large deformations of the isocontours. This strategy limits the number of reinitialization steps and shows a good balance between accuracy and computational cost. Numerical results compare well with usual level set strategies and confirm the necessity of the reinitialization procedure, together with a limited number of reinitialization steps. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
20.
This paper investigates the performance of preconditioned Krylov subspace methods used in a previously presented two‐fluid model developed for the simulation of separated and intermittent gas–liquid flows. The two‐fluid model has momentum and mass balances for each phase. The equations comprising this model are solved numerically by applying a two‐step semi‐implicit time integration procedure. A finite difference numerical scheme with a staggered mesh is used. Previously, the resulting linear algebraic equations were solved by a Gaussian band solver. In this study, these algebraic equations are also solved using the generalized minimum residual (GMRES) and the biconjugate gradient stabilized (Bi‐CGSTAB) Krylov subspace iterative methods preconditioned with incomplete LU factorization using the ILUT(p, τ) algorithm. The decrease in the computational time using the iterative solvers instead of the Gaussian band solver is shown to be considerable. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献