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1.
A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder 下载免费PDF全文
A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM)
is presented in this work. The present approach is an improvement to the conventional
IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately
satisfied. As a result, there is flow penetration to the solid boundary. Another drawback
of conventional IB-LBM is the use of Dirac delta function interpolation, which only has
the first order of accuracy. In this work, the no-slip boundary condition is directly
implemented, and used to correct the velocity at two adjacent mesh points from both
sides of the boundary point. The velocity correction is made through the second-order
polynomial interpolation rather than the first-order delta function interpolation.
Obviously, the two drawbacks of conventional IB-LBM are removed in the present study.
Another important contribution of this paper is to present a simple way to compute the
hydrodynamic forces on the boundary from Newton's second law. To validate the proposed
method, the two-dimensional vortex decaying problem and incompressible flow over a
circular cylinder are simulated. As shown in the present results, the flow penetration
problem is eliminated, and the obtained results compare very well with available data
in the literature. 相似文献
2.
Natural Convection in a Concentric Annulus: A Lattice Boltzmann Method Study with Boundary Condition-Enforced Immersed Boundary Method 下载免费PDF全文
Yang Hu Xiao-Dong Niu Shi Shu Haizhuan Yuan & Mingjun Li 《advances in applied mathematics and mechanics.》2013,5(3):321-336
In this paper, a boundary condition-enforced IBM is introduced into the LBM
in order to satisfy the non-slip and temperature boundary conditions, and natural
convections in a concentric isothermal annulus between a square outer cylinder and a
circular inner cylinder are simulated. The obtained results show that the boundary
condition-enforced method gives a better solution for the flow field and the complicated
physics of the natural convections in the selected case is correctly captured. The
calculated average Nusselt numbers agree well with the previous studies. 相似文献
3.
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations 总被引:1,自引:0,他引:1
Xiaolei Yang Xing Zhang Zhilin Li Guo-Wei He 《Journal of computational physics》2009,228(20):7821-7836
The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations. 相似文献
4.
An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity 总被引:1,自引:0,他引:1
A formally second-order accurate immersed boundary method is presented and tested in this paper. We apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first-order method. The numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high Reynolds number flows with immersed boundaries. 相似文献
5.
We propose a fast and non-stiff approach for the solutions of the Immersed Boundary Method, for Newtonian, incompressible flows in two or three dimensions. The proposed methodology is built on a robust semi-implicit discretization introduced by Peskin in the late 70s which is solved efficiently through the novel use of a fast, treecode strategy to compute flow-structure interactions. Optimal multipole-type expansions are performed numerically by solving a least squares problem with a new, fast iterative algorithm. The new Immersed Boundary Method is particularly well suited for three-dimensional applications and/or for problems where the number of immersed boundary points is large. We demonstrate the efficacy and superiority of the method over existing approaches with two simple but illustrative examples in 3D. 相似文献
6.
7.
Wen Chen & Yan Gu 《advances in applied mathematics and mechanics.》2012,4(5):543-558
This study proposes a new formulation of singular boundary method (SBM)
to solve the 2D potential problems, while retaining its original merits
being free of integration and mesh, easy-to-program, accurate and
mathematically simple without the requirement of a fictitious boundary
as in the method of fundamental solutions (MFS). The key idea of the SBM
is to introduce the concept of the origin intensity factor to isolate the
singularity of fundamental solution so that the source points can be placed
directly on the physical boundary. This paper presents a new approach to
derive the analytical solution of the origin intensity factor based on the
proposed subtracting and adding-back techniques. And the troublesome sample
nodes in the ordinary SBM are avoided and the sample solution is also not
necessary for the Neumann boundary condition. Three benchmark problems are
tested to demonstrate the feasibility and accuracy of the new formulation
through detailed comparisons with the boundary element method (BEM), MFS,
regularized meshless method (RMM) and boundary distributed source (BDS)
method. 相似文献
8.
A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems 下载免费PDF全文
This article extends the finite element method of lines to a parabolic
initial boundary value problem whose diffusion coefficient is discontinuous
across an interface that changes with respect to time. The method presented
here uses immersed finite element (IFE) functions for the discretization in
spatial variables that can be carried out over a fixed mesh (such as a
Cartesian mesh if desired), and this feature makes it possible to reduce
the parabolic equation to a system of ordinary differential equations (ODE)
through the usual semi-discretization procedure. Therefore, with a suitable
choice of the ODE solver, this method can reliably and efficiently solve a
parabolic moving interface problem over a fixed structured (Cartesian) mesh.
Numerical examples are presented to demonstrate features of this new method. 相似文献
9.
We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing immersed boundary methods: the proposed algorithms calculate and apply the force density in the extended solid domain to uphold the solid velocity and hence the boundary condition at the rigid-body surface. The principle of the embedded boundary algorithm allows us to solve the fluid equations on a Cartesian grid with a set of external forces spread onto the grid points occupied by the rigid structure. The proposed algorithms use the MAC (marker and cell) algorithm to solve the incompressible Navier-Stokes equations. Unlike projection methods, the MAC scheme incorporates the gradient of the force density in solving the pressure Poisson equation, so that the dipole force, due to the jump of pressure across the solid-fluid interface, is directly balanced by the gradient of the force density. We validate the proposed algorithms via the classical benchmark problem of flow past a cylinder. Our numerical experiments show that numerical solutions of the velocity field obtained by using the proposed algorithms are smooth across the solid-fluid interface. Finally, we consider the problem of a cylinder moving between two parallel plane walls. Numerical solutions of this problem obtained by using the proposed algorithms are compared with the classical asymptotic solutions. We show that the two solutions are in good agreement. 相似文献
10.
11.
A Numerical Study of Jet Propulsion of an Oblate Jellyfish Using a Momentum Exchange-Based Immersed Boundary-Lattice Boltzmann Method 下载免费PDF全文
Hai-Zhuan Yuan Shi Shu Xiao-Dong Niu Mingjun Li & Yang Hu 《advances in applied mathematics and mechanics.》2014,6(3):307-326
In present paper, the locomotion of an oblate jellyfish is numerically
investigated by using a momentum exchange-based immersed boundary-Lattice
Boltzmann method based on a dynamic model describing the oblate jellyfish.
The present investigation is agreed fairly well with the previous experimental
works. The Reynolds number and the mass density of the jellyfish are found to
have significant effects on the locomotion of the oblate jellyfish. Increasing
Reynolds number, the motion frequency of the jellyfish becomes slow due to the
reduced work done for the pulsations, and decreases and increases before and
after the mass density ratio of the jellyfish to the carried fluid is 0.1. The
total work increases rapidly at small mass density ratios and slowly increases
to a constant value at large mass density ratio. Moreover, as mass density ratio
increases, the maximum forward velocity significantly reduces in the contraction
stage, while the minimum forward velocity increases in the relaxation stage. 相似文献
12.
13.
The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. 相似文献
14.
15.
In this paper, a finite difference code for Direct and Large Eddy Simulation (DNS/LES) of incompressible flows is presented. This code is an intermediate tool between fully spectral Navier–Stokes solvers (limited to academic geometry through Fourier or Chebyshev representation) and more versatile codes based on standard numerical schemes (typically only second-order accurate). The interest of high-order schemes is discussed in terms of implementation easiness, computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations. The equivalence rules between operations in physical and spectral spaces are efficiently used to solve the Poisson equation introduced by the projection method. It is shown that for the pressure treatment, an accurate Fourier representation can be used for more flexible boundary conditions than periodicity or free-slip. Using the concept of the modified wave number, the incompressibility can be enforced up to the machine accuracy. The benefit offered by this alternative method is found to be very satisfactory, even when a formal second-order error is introduced locally by boundary conditions that are neither periodic nor symmetric. The usefulness of high-order schemes combined with an immersed boundary method (IBM) is also demonstrated despite the second-order accuracy introduced by this wall modelling strategy. In particular, the interest of a partially staggered mesh is exhibited in this specific context. Three-dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high-order schemes to reduce the computational cost for a given accuracy. The main conclusion of this paper is that finite difference schemes with quasi-spectral accuracy can be very efficient for DNS/LES of incompressible flows, while allowing flexibility for the boundary conditions and easiness in the code development. Therefore, this compromise fits particularly well for very high-resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments. 相似文献
16.
Robert S. Callihan & Aihua W. Wood 《advances in applied mathematics and mechanics.》2012,4(6):703-718
Here considered is the problem of transient electromagnetic scattering from
overfilled cavities embedded in an impedance ground plane. An artificial boundary
condition is introduced on a semicircle enclosing the cavity that couples the
fields from the infinite exterior domain to those fields inside. A Green's
function solution is obtained for the exterior domain, while the interior problem
is solved using finite element method. Well-posedness of the associated variational
formulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method. 相似文献
17.
Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions 下载免费PDF全文
In this paper, we present two-level defect-correction finite element method
for steady Navier-Stokes equations at high Reynolds number with the friction boundary
conditions, which results in a variational inequality problem of the second kind.
Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes
type on the coarse mesh and solve a variational inequality problem of Navier-Stokes
type corresponding to Newton linearization on the fine mesh. The error estimates
for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived.
Finally, the numerical results are provided to confirm our theoretical analysis. 相似文献
18.
Iterative Method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation 下载免费PDF全文
The solution of boundary value problems (BVP) for fourth order
differential equations by their reduction to BVP for second order
equations, with the aim to use the available efficient algorithms
for the latter ones, attracts attention from many researchers. In
this paper, using the technique developed by the authors in recent
works we construct iterative method for a problem with complicated
mixed boundary conditions for biharmonic equation which is
originated from nanofluidic physics. The convergence rate of the
method is proved and some numerical experiments are performed for
testing its dependence on a parameter appearing in boundary
conditions and on the position of the point where a transmission of
boundary conditions occurs. 相似文献
19.
20.
Analysis for Transmission Characteristics of Closed Trapezoidal-Groove Waveguide with Boundary Element Method 总被引:1,自引:0,他引:1
Fuyong Xu Xiaohui Lin Bin You 《International Journal of Infrared and Millimeter Waves》1999,20(9):1691-1699
In this paper, the cut-off and dispersion characteristics of a new kind of closed trapezoidal-groove waveguide that has more advantages than open groove waveguides are analyzed with the help of the boundary element method, the relationship between cut-off wavelengths and variations of guide's relative sizes is discussed in detail. The calculated results are in good agreement with those in the relevant reference. So, the obtained conclusions are very important in theoretical studies and actual applications of closed trapezoidal-groove waveguides for millimeter and submillimeter waves. 相似文献