共查询到20条相似文献,搜索用时 15 毫秒
1.
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-type method. The numerical results show that the overall scheme is second order
accuracy. 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. 相似文献
2.
An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary. In this approach, the normal derivative of the pressure along the parts of the boundary is introduced as an additional variable and it is solved by the GMRES iterative method. The dimension of the augmented variable in discretization is the number of grid points along the boundary which is O(N). Each GMRES iteration (or one matrix-vector multiplication) requires three fast Poisson solvers for the pressure and the velocity. In our numerical experiments, only a few iterations are needed. We have also combined the augmented approach for Stokes equations involving interfaces, discontinuities, and singularities. 相似文献
3.
The level set method is one of the most successful methods for the simulation
of multi-phase flows. To keep the level set function close the signed distance function,
the level set function is constantly reinitialized by solving a Hamilton-Jacobi type
of equation during the simulation. When the fluid interface intersects with a solid wall,
a moving contact line forms and the reinitialization of the level set function requires
a boundary condition in certain regions on the wall. In this work, we propose to use
the dynamic contact angle, which is extended from the contact line, as the boundary
condition for the reinitialization of the level set function. The reinitialization equation
and the equation for the normal extension of the dynamic contact angle form a coupled
system and are solved simultaneously. The extension equation is solved on the
wall and it provides the boundary condition for the reinitialization equation; the level
set function provides the directions along which the contact angle is extended from
the contact line. The coupled system is solved using the 3rd order TVD Runge-Kutta
method and the Godunov scheme. The Godunov scheme automatically identifies the
regions where the angle condition needs to be imposed. The numerical method is illustrated
by examples in three dimensions. 相似文献
4.
An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Wei-Fan Hu Te-Sheng Lin Yu-Hau Tseng & Ming-Chih Lai 《Communications In Computational Physics》2023,33(4):1090-1105
A new and efficient neural-network and finite-difference hybrid method is
developed for solving Poisson equation in a regular domain with jump discontinuities
on embedded irregular interfaces. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional
treatment accounting for the jump discontinuities must be employed. Here, we aim to
elevate such an extra effort to ease our implementation by machine learning methodology. The key idea is to decompose the solution into singular and regular parts. The
neural network learning machinery incorporating the given jump conditions finds the
singular solution, while the standard five-point Laplacian discretization is used to obtain the regular solution with associated boundary conditions. Regardless of the interface geometry, these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation, making the hybrid method easy
to implement and efficient. The two- and three-dimensional numerical results show
that the present hybrid method preserves second-order accuracy for the solution and
its derivatives, and it is comparable with the traditional immersed interface method in
the literature. As an application, we solve the Stokes equations with singular forces to
demonstrate the robustness of the present method. 相似文献
5.
Pseudostress-Based Mixed Finite Element Methods for the Stokes Problem in Rn with Dirichlet Boundary Conditions I: A Priori Error Analysis
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Gabriel N. Gatica Antonio Má rquez & Manuel A. Sá nchez 《Communications In Computational Physics》2012,12(1):109-134
We consider a non-standard mixed method for the Stokes problem in Rn, n∈{2,3}, with Dirichlet boundary conditions, in which, after using the incompressibility condition to eliminate the pressure, the pseudostress tensor σ and the velocity vectorubecome the only unknowns. Then, we apply the Babuška-Brezzi theory to prove the well-posedness of the corresponding continuous and discrete formulations. In particular, we show that Raviart-Thomas elements of order k≥0 for σ and piecewise polynomials of degree k foruensure unique solvability and stability of the associated Galerkin scheme. In addition, we introduce and analyze an augmented approach for our pseudostress-velocity formulation. The methodology employed is based on the introduction of the Galerkin least-squares type terms arising from the constitutive and equilibrium equations, and the Dirichlet boundary condition for the velocity, all of them multiplied by suitable stabilization parameters. We show that these parameters can be chosen so that the resulting augmented variational formulation is defined by a strongly coercive bilinear form, whence the associated Galerkin scheme becomes well posed for any choice of finite element subspaces. For instance, Raviart-Thomas elements of order k≥0 for σ and continuous piecewise polynomials of degree k+1 forubecome a feasible choice in this case. Finally, become a feasible choice in this case. Finally, extensive numerical experiments illustrating the good performance of the methods and comparing them with other procedures available in the literature, are provided. 相似文献
6.
A front tracking method combined with the real ghost fluid method (RGFM)
is proposed for simulations of fluid interfaces in two-dimensional compressible flows.
In this paper the Riemann problem is constructed along the normal direction of interface
and the corresponding Riemann solutions are used to track fluid interfaces. The
interface boundary conditions are defined by the RGFM, and the fluid interfaces are
explicitly tracked by several connected marker points. The Riemann solutions are also
used directly to update the flow states on both sides of the interface in the RGFM.
In order to validate the accuracy and capacity of the new method, extensive numerical
tests including the bubble advection, the Sod tube, the shock-bubble interaction,
the Richtmyer-Meshkov instability and the gas-water interface, are simulated by using
the Euler equations. The computational results are also compared with earlier computational
studies and it shows good agreements including the compressible gas-water
system with large density differences. 相似文献
7.
A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In multi-physics computations where a compressible fluid is coupled with
a linearly elastic solid, it is standard to enforce continuity of the normal velocities and
of the normal stresses at the interface between the fluid and the solid. In a numerical
scheme, there are many ways that velocity- and stress-continuity can be enforced in
the discrete approximation. This paper performs a normal mode stability analysis of
the linearized problem to investigate the stability of different numerical interface conditions
for a model problem approximated by upwind type finite difference schemes.
The analysis shows that depending on the ratio of densities between the solid and
the fluid, some numerical interface conditions are stable up to the maximal CFL-limit,
while other numerical interface conditions suffer from a severe reduction of the stable
CFL-limit. The paper also presents a new interface condition, obtained as a simplified
characteristic boundary condition, that is proved to not suffer from any reduction of
the stable CFL-limit. Numerical experiments in one space dimension show that the
new interface condition is stable also for computations with the non-linear Euler equations
of compressible fluid flow coupled with a linearly elastic solid. 相似文献
8.
An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Zhijun Tan K. M. Lim B. C. Khoo & Desheng Wang 《Communications In Computational Physics》2009,6(5):997-1021
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. 相似文献
9.
A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Jian-Jun Xu Yunqing Huang Ming-Chih Lai & Zhilin Li 《Communications In Computational Physics》2014,15(2):451-469
In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersed
interface method (IIM) for solving Stokes equations with jumps across the interface
and a 3D level-set method for solving the surfactant convection-diffusion equation
along a moving and deforming interface. The 3D IIM Poisson solver modifies the one
in the literature by assuming that the jump conditions of the solution and the flux
are implicitly given at the grid points in a small neighborhood of the interface. This
assumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface.
The interface jump relations are re-derived accordingly. A novel rotational procedure
is given to generate smooth local coordinate systems and make effective interpolation.
Numerical examples demonstrate that the IIM Poisson solver and the Stokes solver
achieve second-order accuracy. A 3D drop with insoluble surfactant under shear flow
is investigated numerically by studying the influences of different physical parameters
on the drop deformation. 相似文献
10.
In this paper, first- and second-order necessary conditions for optimality are studied for a domain optimization problem. The optimization problem considered is the minimization of an objective function defined on the domain boundary through the solution of a boundary value problem. In order to derive the first and second variations of the objective function due to boundary variation, the first and second variations of the solution of the boundary value problem are calculated using a perturbation technique. An iterative shape optimization algorithm for potential flow problems in R2 with Dirichlet boundary conditions is presented. In the algorithm a boundary element method (BEM) is employed to solve the Laplace equation numerically. The validity and accuracy of the algorithm have been verified on a problem where the final solution is known. Finally, the problem of designing a 90° bend for two-dimensional potential flow is solved. 相似文献
11.
This paper presents a fourth-order Cartesian grid based boundary integral
method (BIM) for heterogeneous interface problems in two and three dimensional
space, where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions. The method reformulates the
governing equation with interface conditions into boundary integral equations (BIEs)
and reinterprets the involved integrals as solutions to some simple interface problems
in an extended regular region. Solution of the simple equivalent interface problems for
integral evaluation relies on a fourth-order finite difference method with an FFT-based
fast elliptic solver. The structure of the coefficient matrix is preserved even with the
existence of the interface. In the whole calculation process, analytical expressions of
Green’s functions are never determined, formulated or computed. This is the novelty
of the proposed kernel-free boundary integral (KFBI) method. Numerical experiments
in both two and three dimensions are shown to demonstrate the algorithm efficiency
and solution accuracy even for problems with a large diffusion coefficient ratio. 相似文献
12.
Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Sheri L. Martinelli 《Communications In Computational Physics》2013,14(2):509-536
We study the simulation of specular reflection in a level set method implementation
for wavefront propagation in high frequency acoustics using WENO spatial
operators. To implement WENO efficiently and maintain convergence rate, a rectangular
grid is used over the physical space. When the physical domain does not conform to
the rectangular grid, appropriate boundary conditions to represent reflection must be
derived to apply at grid locations that are not coincident with the reflecting boundary.
A related problem is the extraction of the normal vectors to the boundary, which is required to formulate the reflection condition. A separate level set method is applied
to pre-compute the boundary normals which are then stored for use in the wavefront
method. Two approaches to handling the reflection boundary condition are proposed
and studied: one uses an approximation to the boundary location, and the other uses
a local reflection principle. The second method is shown to produce superior results. 相似文献
13.
The Immersed Interface Method for Non-Smooth Rigid Objects in Incompressible Viscous Flows
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Yang Liu & Sheng Xu 《Communications In Computational Physics》2021,29(2):510-533
In the immersed interface method, an object in a flow is formulated as a singular force, and jump conditions caused by the singular force are incorporated into numerical schemes to compute the flow. Previous development of the method considered
only smooth objects. We here extend the method to handle non-smooth rigid objects
with sharp corners in 2D incompressible viscous flows. We represent the boundary of
an object as a polygonal curve moving through a fixed Cartesian grid. We compute
necessary jump conditions to achieve boundary condition capturing on the object. We
incorporate the jump conditions into finite difference schemes to solve the flow on the
Cartesian grid. The accuracy, efficiency and robustness of our method are tested using
canonical flow problems. The results demonstrate that the method has second-order
accuracy for the velocity and first-order accuracy for the pressure in the infinity norm,
and is extremely efficient and robust to simulate flows around non-smooth complex
objects. 相似文献
14.
Yongyue Jiang Ping Lin Zhenlin Guo & Shuangling Dong 《Communications In Computational Physics》2015,18(1):180-202
In this paper, we compute a phase field (diffuse interface) model of Cahn-Hilliard
type for moving contact line problems governing the motion of isothermal
multiphase incompressible fluids. The generalized Navier boundary condition proposed
by Qian et al. [1] is adopted here. We discretize model equations using a continuous
finite element method in space and a modified midpoint scheme in time. We
apply a penalty formulation to the continuity equation which may increase the stability
in the pressure variable. Two kinds of immiscible fluids in a pipe and droplet displacement
with a moving contact line under the effect of pressure driven shear flow
are studied using a relatively coarse grid. We also derive the discrete energy law for
the droplet displacement case, which is slightly different due to the boundary conditions.
The accuracy and stability of the scheme are validated by examples, results and
estimate order. 相似文献
15.
An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Yang Hu Decai Li Shi Shu & Xiaodong Niu 《Communications In Computational Physics》2016,20(5):1210-1257
In this paper, a diffuse-interface immersed boundary method (IBM) is proposed
to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin)
in thermal flow problems. The novel IBM is implemented combining with the lattice
Boltzmann method (LBM). The present algorithm enforces the three types of thermal
boundary conditions at the boundary points. Concretely speaking, the IBM for the
Dirichlet boundary condition is implemented using an iterative method, and its main
feature is to accurately satisfy the given temperature on the boundary. The Neumann
and Robin boundary conditions are implemented in IBM by distributing the jump of
the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained
by applying the jump interface conditions in the normal and tangential directions. A
simple analysis of the computational accuracy of IBM is developed. The analysis indicates
that the Taylor-Green vortices problem which was used in many previous studies
is not an appropriate accuracy test example. The capacity of the present thermal immersed
boundary method is validated using four numerical experiments: (1) Natural
convection in a cavity with a circular cylinder in the center; (2) Flows over a heated
cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation
of a single isothermal cold particle in a vertical channel. The numerical
results show good agreements with the data in the previous literatures. 相似文献
16.
A Fourth-Order Upwinding Embedded Boundary Method (UEBM) for Maxwell's Equations in Media with Material Interfaces: Part I
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, we present a new fourth-order upwinding embedded boundary method (UEBM) over Cartesian grids, originally proposed in the Journal of Computational Physics [190 (2003), pp. 159-183.] as a second-order method for treating material interfaces for Maxwell's equations. In addition to the idea of the UEBM to evolve solutions at interfaces, we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces. As a result, Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method, in contrast to the original second-order UEBM based on a Lax-Wendroff type difference. The final scheme allows time step sizes independent of the interface locations. Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method. We tested the scheme for several wave problems with various material interface locations, including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis. 相似文献
17.
A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
S. Kelbij Star Giovanni Stabile Francesco Belloni Gianluigi Rozza & Joris Degroote 《Communications In Computational Physics》2021,30(1):34-66
A Finite-Volume based POD-Galerkin reduced order model is developed for
fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method,
whose aim is to obtain homogeneous basis functions for the reduced basis space and
the penalty method where the boundary conditions are enforced in the reduced order
model using a penalty factor. The penalty method is improved by using an iterative
solver for the determination of the penalty factor rather than tuning the factor with a
sensitivity analysis or numerical experimentation.The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet
channels and one outlet channel. The results show that the boundaries of the reduced
order model can be controlled with the boundary control methods and the same order
of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order
models are 270-308 times faster than the full order models for the lid driven cavity test
case and 13-24 times for the Y-junction test case. 相似文献
18.
We develop a continuum hydrodynamic model for two-phase immiscible
flows that involve electroosmotic effect in an electrolyte and moving contact line at
solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in
the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333–360
(2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach
is applied here to the derivation of the continuum hydrodynamic model for charged
two-phase immiscible flows where one fluid component is an electrolyte exhibiting
electroosmotic effect on a charged surface. A phase field is employed to model the
diffuse interface between two immiscible fluid components, one being the electrolyte
and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model
consists of the incompressible Navier-Stokes equation for momentum transport, the
Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for
interface motion, and the Poisson equation for electric potential, along with all the
necessary boundary conditions. In particular, all the dynamic boundary conditions at
solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples
in two-dimensional space, which involve overlapped electric double layer fields, have
been presented to demonstrate the validity and applicability of the model, and a few
salient features of the two-phase immiscible electroosmotic flows at solid surface. The
wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric
double layer are both investigated. 相似文献
19.
A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this article, we discuss a least-squares/fictitious domain method for the
solution of linear elliptic boundary value problems with Robin boundary conditions.
Let Ω and ω be two bounded domains of Rdsuch that ω⊂Ω. For a linear elliptic problem
in Ω\ω with Robin boundary condition on the boundary γ of ω, our goal here is to
develop a fictitious domain method where one solves a variant of the original problem
on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual
control type and relies on a least-squares formulation making the problem solvable by
a conjugate gradient algorithm operating in a well chosen control space. Numerical results
obtained when applying our method to the solution of two-dimensional elliptic
and parabolic problems are given; they suggest optimal order of convergence. 相似文献
20.
Within the projection schemes for the incompressible Navier-Stokes equations
(namely "pressure-correction" method), we consider the simplest method (of order
one in time) which takes into account the pressure in both steps of the splitting
scheme. For this scheme, we construct, analyze and implement a new high order compact
spatial approximation on nonstaggered grids. This approach yields a fourth order
accuracy in space with an optimal treatment of the boundary conditions (without error
on the velocity) which could be extended to more general splitting. We prove the
unconditional stability of the associated Cauchy problem via von Neumann analysis.
Then we carry out a normal mode analysis so as to obtain more precise results about
the behavior of the numerical solutions. Finally we present detailed numerical tests for
the Stokes and the Navier-Stokes equations (including the driven cavity benchmark)
to illustrate the theoretical results. 相似文献