共查询到20条相似文献,搜索用时 15 毫秒
1.
Simulation of Incompressible Free Surface Flow Using the Volume Preserving Level Set Method 下载免费PDF全文
This study aims to develop a numerical scheme in collocated Cartesian grids
to solve the level set equation together with the incompressible two-phase flow equations.
A seventh-order accurate upwinding combined compact difference (UCCD7)
scheme has been developed for the approximation of the first-order spatial derivative
terms shown in the level set equation. Developed scheme has a higher accuracy with a
three-point grid stencil to minimize phase error. To preserve the mass of each phase all
the time, the temporal derivative term in the level set equation is approximated by the
sixth-order accurate symplectic Runge-Kutta (SRK6) scheme. All the simulated results
for the dam-break, Rayleigh-Taylor instability, bubble rising, two-bubble merging, and
milkcrown problems in two and three dimensions agree well with the available numerical
or experimental results. 相似文献
2.
Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels 下载免费PDF全文
Tony W. H. Sheu Yogesh G. Bhumkar S. T. Yuan & S. C. Syue 《Communications In Computational Physics》2016,19(2):496-533
A high-order finite difference scheme has been developed to approximate
the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations
and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution
profiles are resolved by using the combined compact difference (CCD) scheme
developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the
second-order derivative terms while a seventh-order accuracy for the first-order derivative
terms. PNP-NS equations have been also transformed to the curvilinear coordinate
system to study the effects of channel shapes on the development of electroosmotic
flow. In this study, the developed scheme has been analyzed rigorously through
the modified equation analysis. In addition, the developed method has been computationally
verified through four problems which are amenable to their own exact solutions.
The electroosmotic flow details in planar and wavy channels have been explored
with the emphasis on the formation of Coulomb force. Significance of different forces
resulting from the pressure gradient, diffusion and Coulomb origins on the convective
electroosmotic flow motion is also investigated in detail. 相似文献
3.
An Interface-Capturing Method for Resolving Compressible Two-Fluid Flows with General Equation of State 下载免费PDF全文
T. S. Lee J. G. Zheng & S. H. Winoto 《Communications In Computational Physics》2009,6(5):1137-1162
In this study, a stable and robust interface-capturing method is developed
to resolve inviscid, compressible two-fluid flows with general equation of state (EOS).
The governing equations consist of mass conservation equation for each fluid, momentum
and energy equations for mixture and an advection equation for volume fraction
of one fluid component. Assumption of pressure equilibrium across an interface is
used to close the model system. MUSCL-Hancock scheme is extended to construct
input states for Riemann problems, whose solutions are calculated using generalized
HLLC approximate Riemann solver. Adaptive mesh refinement (AMR) capability is
built into hydrodynamic code. The resulting method has some advantages. First, it is
very stable and robust, as the advection equation is handled properly. Second, general
equation of state can model more materials than simple EOSs such as ideal and
stiffened gas EOSs for example. In addition, AMR enables us to properly resolve flow
features at disparate scales. Finally, this method is quite simple, time-efficient and easy
to implement. 相似文献
4.
Development of a Volume of Fluid Method for Computing Interfacial Incompressible Fluid Flows 下载免费PDF全文
Zhenghua Gu Yuan Yao Ching-Hao Yu & Ruidong An 《Communications In Computational Physics》2020,27(4):1076-1114
This study is aimed to develop a volume of fluid (VOF) method to capture
the free surface flow. The incompressible two-phase flow is computed by second-order
Adams-Bashforth algorithm with a uniform staggered Cartesian grid arrangement.
The tangent of hyperbola for interface capturing (THINC) scheme and weighted linear
interface calculation (WLIC) based geometrical reconstruction procedure have been
implemented in the operator-splitting method for the VOF method. The proposed
VOF method preserves mass well, and the interface normal vector can be easily estimated from the level set (LS) function. The LS function, which is a continuous signed
distance function around the interface, is represented by solving the re-initialization
equation. Numerical results using the present scheme are compared with experimental data and other numerical results in the Rayleigh-Taylor instability, dam-break flow,
travelling solitary wave, Kelvin-Helmholtz instability, rising bubble and merging bubble problems. We also present numerical results in detail between computations made
with the proposed VOF method and computations made with the conventional LS
method. 相似文献
5.
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
6.
Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation 下载免费PDF全文
In this paper, we propose a new conservative semi-Lagrangian (SL) finite
difference (FD) WENO scheme for linear advection equations, which can serve as a
base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure
in the proposed SL FD scheme is the same as the one used in the SL finite volume
(FV) WENO scheme [3]. However, instead of inputting cell averages and approximate
the integral form of the equation in a FV scheme, we input point values and approximate
the differential form of equation in a FD spirit, yet retaining very high order
(fifth order in our experiment) spatial accuracy. The advantage of using point values,
rather than cell averages, is to avoid the second order spatial error, due to the shearing
in velocity (v) and electrical field (E) over a cell when performing the Strang splitting
to the Vlasov equation. As a result, the proposed scheme has very high spatial accuracy,
compared with second order spatial accuracy for Strang split SL FV scheme for
solving the Vlasov-Poisson (VP) system. We perform numerical experiments on linear
advection, rigid body rotation problem; and on the Landau damping and two-stream
instabilities by solving the VP system. For comparison, we also apply (1) the conservative
SL FD WENO scheme, proposed in [22] for incompressible advection problem, (2)
the conservative SL FD WENO scheme proposed in [21] and (3) the non-conservative
version of the SL FD WENO scheme in [3] to the same test problems. The performances
of different schemes are compared by the error table, solution resolution of sharp interface,
and by tracking the conservation of physical norms, energies and entropies,
which should be physically preserved. 相似文献
7.
A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces 下载免费PDF全文
Guang Lin Jie Bao Zhijie Xu Alexandre M. Tartakovsky & Charles H. Henager Jr. 《Communications In Computational Physics》2014,15(1):76-92
In this study, we present a new numerical model for crystal growth in a
vertical solidification system. This model takes into account the buoyancy induced
convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice
kinetics solver based on the Boltzmann equation is employed to model the unsteady
incompressible flow. This model is used to investigate the effect of furnace operational
conditions on crystal growth interface profiles and growth velocities. For a simple
case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature
boundary conditions, the heat transport in the melt near the phase interface is diffusion
dominant and advection is suppressed. 相似文献
8.
Development of a Combined Compact Difference Scheme to Simulate Soliton Collision in a Shallow Water Equation 下载免费PDF全文
In this paper a three-step scheme is applied to solve the Camassa-Holm
(CH) shallow water equation. The differential order of the CH equation has been
reduced in order to facilitate development of numerical scheme in a comparatively
smaller grid stencil. Here a three-point seventh-order spatially accurate upwinding
combined compact difference (CCD) scheme is proposed to approximate the first-order
derivative term. We conduct modified equation analysis on the CCD scheme and
eliminate the leading discretization error terms for accurately predicting unidirectional
wave propagation. The Fourier analysis is carried out as well on the proposed numerical
scheme to minimize the dispersive error. For preserving Hamiltonians in Camassa-Holm
equation, a symplecticity conserving time integrator has been employed. The
other main emphasis of the present study is the use of u−P−α formulation to get nondissipative
CH solution for peakon-antipeakon and soliton-anticuspon head-on wave
collision problems. 相似文献
9.
Construction,Analysis and Application of Coupled Compact Difference Scheme in Computational Acoustics and Fluid Flow Problems 下载免费PDF全文
Jitenjaya Pradhan Amit Bikash Mahato Satish D. Dhandole & Yogesh G. Bhumkar 《Communications In Computational Physics》2015,18(4):957-984
In the present work, a new type of coupled compact difference scheme has
been proposed for the solution of computational acoustics and flow problems. The
proposed scheme evaluates the first, the second and the fourth derivative terms simultaneously.
Derived compact difference scheme has a significant spectral resolution and
a physical dispersion relation preserving (DRP) ability over a considerable wavenumber
range when a fourth order four stage Runge-Kutta scheme is used for the time
integration. Central stencil has been used for the present numerical scheme to evaluate
spatial derivative terms. Derived scheme has the capability of adding numerical
diffusion adaptively to attenuate spurious high wavenumber oscillations responsible
for numerical instabilities. The DRP nature of the proposed scheme across a wider
wavenumber range provides accurate results for the model wave equations as well
as computational acoustic problems. In addition to the attractive feature of adaptive
diffusion, present scheme also helps to control spurious reflections from the domain
boundaries and is projected as an alternative to the perfectly matched layer (PML)
technique. 相似文献
10.
Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows 下载免费PDF全文
Yuan Gao Liuming Yang Yang Yu Guoxiang Hou & Zhongbao Hou 《Communications In Computational Physics》2021,30(5):1427-1452
Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose
a consistent forcing scheme in SLBM for incompressible flows with external forces. The
lattice discrete effects are considered at the level of distribution functions in the present
forcing scheme. Consequently, it is more accurate compared with the original forcing
scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE)
expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved
through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme,
we simulate with multiple forms of external force interactions including the space- and
time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed
in the present scheme even when a coarse mesh is applied while the original scheme
fails. Excellent agreements between the analytical solutions and our numerical results
can be observed. 相似文献
11.
A Compact Third-Order Gas-Kinetic Scheme for Compressible Euler and Navier-Stokes Equations 下载免费PDF全文
In this paper, a compact third-order gas-kinetic scheme is proposed for the
compressible Euler and Navier-Stokes equations. The main reason for the feasibility
to develop such a high-order scheme with compact stencil, which involves only
neighboring cells, is due to the use of a high-order gas evolution model. Besides the
evaluation of the time-dependent flux function across a cell interface, the high-order
gas evolution model also provides an accurate time-dependent solution of the flow
variables at a cell interface. Therefore, the current scheme not only updates the cell
averaged conservative flow variables inside each control volume, but also tracks the
flow variables at the cell interface at the next time level. As a result, with both cell averaged
and cell interface values, the high-order reconstruction in the current scheme
can be done compactly. Different from using a weak formulation for high-order accuracy
in the Discontinuous Galerkin method, the current scheme is based on the strong
solution, where the flow evolution starting from a piecewise discontinuous high-order
initial data is precisely followed. The cell interface time-dependent flow variables can
be used for the initial data reconstruction at the beginning of next time step. Even with
compact stencil, the current scheme has third-order accuracy in the smooth flow regions,
and has favorable shock capturing property in the discontinuous regions. It can
be faithfully used from the incompressible limit to the hypersonic flow computations,
and many test cases are used to validate the current scheme. In comparison with many
other high-order schemes, the current method avoids the use of Gaussian points for
the flux evaluation along the cell interface and the multi-stage Runge-Kutta time stepping
technique. Due to its multidimensional property of including both derivatives of
flow variables in the normal and tangential directions of a cell interface, the viscous
flow solution, especially those with vortex structure, can be accurately captured. With
the same stencil of a second order scheme, numerical tests demonstrate that the current
scheme is as robust as well-developed second-order shock capturing schemes, but
provides more accurate numerical solutions than the second order counterparts. 相似文献
12.
An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains 下载免费PDF全文
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
13.
S. C. Fu R. M. C. So & W. W. F. Leung 《Communications In Computational Physics》2011,9(5):1257-1283
The objective of this paper is to seek an alternative to the numerical simulation
of the Navier-Stokes equations by a method similar to solving the BGK-type
modeled lattice Boltzmann equation. The proposed method is valid for both gas and
liquid flows. A discrete flux scheme (DFS) is used to derive the governing equations
for two distribution functions; one for mass and another for thermal energy. These
equations are derived by considering an infinitesimally small control volume with a
velocity lattice representation for the distribution functions. The zero-order moment
equation of the mass distribution function is used to recover the continuity equation,
while the first-order moment equation recovers the linear momentum equation. The
recovered equations are correct to the first order of the Knudsen number (Kn); thus,
satisfying the continuum assumption. Similarly, the zero-order moment equation of
the thermal energy distribution function is used to recover the thermal energy equation.
For aerodynamic flows, it is shown that the finite difference solution of the DFS
is equivalent to solving the lattice Boltzmann equation (LBE) with a BGK-type model
and a specified equation of state. Thus formulated, the DFS can be used to simulate a
variety of aerodynamic and hydrodynamic flows. Examples of classical aeroacoustics,
compressible flow with shocks, incompressible isothermal and non-isothermal Couette
flows, stratified flow in a cavity, and double diffusive flow inside a rectangle are used
to demonstrate the validity and extent of the DFS. Very good to excellent agreement
with known analytical and/or numerical solutions is obtained; thus lending evidence
to the DFS approach as an alternative to solving the Navier-Stokes equations for fluid
flow simulations. 相似文献
14.
An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids 下载免费PDF全文
Zhijun Tan D. V. Le K. M. Lim & B. C. Khoo 《Communications In Computational Physics》2012,11(3):925-950
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. 相似文献
15.
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
16.
Development of an Explicit Symplectic Scheme that Optimizes the Dispersion-Relation Equation of the Maxwell's Equations 下载免费PDF全文
Tony W. H. Sheu L. Y. Liang & J. H. Li 《Communications In Computational Physics》2013,13(4):1107-1133
In this paper an explicit finite-difference time-domain scheme for solving
the Maxwell's equations in non-staggered grids is presented. The proposed scheme
for solving the Faraday's and Ampère's equations in a theoretical manner is aimed to
preserve discrete zero-divergence for the electric and magnetic fields. The inherent local conservation laws in Maxwell's equations are also preserved discretely all the time
using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme.
The remaining spatial derivative terms in the semi-discretized Faraday's and Ampère's
equations are then discretized to provide an accurate mathematical dispersion relation
equation that governs the numerical angular frequency and the wavenumbers in two
space dimensions. To achieve the goal of getting the best dispersive characteristics, we
propose a fourth-order accurate space centered scheme which minimizes the difference
between the exact and numerical dispersion relation equations. Through the computational exercises, the proposed dual-preserving solver is computationally demonstrated
to be efficient for use to predict the long-term accurate Maxwell's solutions. 相似文献
17.
Andrea Thomann Markus Zenk Gabriella Puppo & Christian Klingenberg 《Communications In Computational Physics》2020,28(2):591-620
We present an implicit-explicit finite volume scheme for the Euler equations.
We start from the non-dimensionalised Euler equations where we split the pressure in
a slow and a fast acoustic part. We use a Suliciu type relaxation model which we split
in an explicit part, solved using a Godunov-type scheme based on an approximate
Riemann solver, and an implicit part where we solve an elliptic equation for the fast
pressure. The relaxation source terms are treated projecting the solution on the equilibrium manifold. The proposed scheme is positivity preserving with respect to the
density and internal energy and asymptotic preserving towards the incompressible
Euler equations. For this first order scheme we give a second order extension which
maintains the positivity property. We perform numerical experiments in 1D and 2D to
show the applicability of the proposed splitting and give convergence results for the
second order extension. 相似文献
18.
Finite Volume Lattice Boltzmann Method for Nearly Incompressible Flows on Arbitrary Unstructured Meshes 下载免费PDF全文
A genuine finite volume method based on the lattice Boltzmann equation
(LBE) for nearly incompressible flows is developed. The proposed finite volume lattice
Boltzmann method (FV-LBM) is grid-transparent, i.e., it requires no knowledge of
cell topology, thus it can be implemented on arbitrary unstructured meshes for effective
and efficient treatment of complex geometries. Due to the linear advection term in
the LBE, it is easy to construct multi-dimensional schemes. In addition, inviscid and
viscous fluxes are computed in one step in the LBE, as opposed to in two separate steps
for the traditional finite-volume discretization of the Navier-Stokes equations. Because
of its conservation constraints, the collision term of the kinetic equation can be treated
implicitly without linearization or any other approximation, thus the computational
efficiency is enhanced. The collision with multiple-relaxation-time (MRT) model is
used in the LBE. The developed FV-LBM is of second-order convergence. The proposed
FV-LBM is validated with three test cases in two-dimensions: (a) the Poiseuille
flow driven by a constant body force; (b) the Blasius boundary layer; and (c) the steady
flow past a cylinder at the Reynolds numbers Re=10, 20, and 40. The results verify the
designed accuracy and efficacy of the proposed FV-LBM. 相似文献
19.
A finite volume-based computational model was developed to investigate the uniformity of the fluid flow across the hollow fiber membranes in blood oxygenation devices. A two-dimensional annular cross section of a blood oxygenation device including about 3,300 hollow fiber membranes was used in the computation model. The equations governing the steady incompressible laminar flow in the blood oxygenation device were solved numerically and the results were compared with those obtained from the equivalent porous medium approximation. For the porous medium approximation, the Ergun equation was used for evaluating the permeability. The simulation results showed that the fluid molecules spend about six times longer in the fiber bundle region than that in its equivalent porous medium approximation model. The computational model also provides a more detailed fluid flow pattern in the membrane compartment of the blood oxygenator. 相似文献
20.
Two-Grid Method for Miscible Displacement Problem by Mixed Finite Element Methods and Mixed Finite Element Method of Characteristics 下载免费PDF全文
The miscible displacement of one incompressible fluid by another in a porous
medium is governed by a system of two equations. One is elliptic form equation for
the pressure and the other is parabolic form equation for the concentration of one of
the fluids. Since only the velocity and not the pressure appears explicitly in the concentration
equation, we use a mixed finite element method for the approximation of
the pressure equation and mixed finite element method with characteristics for the
concentration equation. To linearize the mixed-method equations, we use a two-grid
algorithm based on the Newton iteration method for this full discrete scheme problems.
First, we solve the original nonlinear equations on the coarse grid, then, we
solve the linearized problem on the fine grid used Newton iteration once. It is shown
that the coarse grid can be much coarser than the fine grid and achieve asymptotically
optimal approximation as long as the mesh sizes satisfy $h=H^2$ in this paper. Finally,
numerical experiment indicates that two-grid algorithm is very effective. 相似文献