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1.
A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction 下载免费PDF全文
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
2.
A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows 下载免费PDF全文
Angela Ferrari Claus-Dieter Munz & Bernhard Weigand 《Communications In Computational Physics》2011,9(1):205-230
In this paper, a new sharp-interface approach to simulate compressible
multiphase flows is proposed. The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order path-conservative
discontinuous Galerkin finite element scheme to evolve an indicator function
that tracks the material interface. At the interface our method applies ghost cells
to compute the numerical flux, as the ghost fluid method. However, unlike the original
ghost fluid scheme of Fedkiw et al. [15], the state of the ghost fluid is derived
from an approximate-state Riemann solver, similar to the approach proposed in [25],
but based on a much simpler formulation. Our formulation leads only to one single
scalar nonlinear algebraic equation that has to be solved at the interface, instead of
the system used in [25]. Away from the interface, we use the new general Osher-type
flux recently proposed by Dumbser and Toro [13], which is a simple but complete Riemann
solver, applicable to general hyperbolic conservation laws. The time integration
is performed using a fully-discrete one-step scheme, based on the approaches recently
proposed in [5, 7]. This allows us to evolve the system also with time-accurate local
time stepping. Due to the sub-cell resolution and the subsequent more restrictive
time-step constraint of the DG scheme, a local evolution for the indicator function is
applied, which is matched with the finite volume scheme for the solution of the Euler
equations that runs with a larger time step. The use of a locally optimal time step
avoids the introduction of excessive numerical diffusion in the finite volume scheme.
Two different fluids have been used, namely an ideal gas and a weakly compressible
fluid modeled by the Tait equation. Several tests have been computed to assess the
accuracy and the performance of the new high order scheme. A verification of our
algorithm has been carefully carried out using exact solutions as well as a comparison
with other numerical reference solutions. The material interface is resolved sharply
and accurately without spurious oscillations in the pressure field. 相似文献
3.
An Approximate Riemann Solver for Fluid-Solid Interaction Problems with Mie-Grüneisen Equations of State 下载免费PDF全文
We propose an approximate solver for compressible fluid-elastoplastic solid Riemann problems. The fluid and hydrostatic components of the solid are described by a family of general Mie-Grüneisen equations of state, and the hypo-elastoplastic constitutive law we studied includes the perfect plasticity and linearly hardened plasticity. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are verified with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, underground explosion and high speed impact applications, are presented to validate the approximate solver. 相似文献
4.
Liang Xu Chengliang Feng & Tiegang Liu 《Communications In Computational Physics》2016,20(3):619-659
The modified ghost fluid method (MGFM), due to its reasonable treatment
for ghost fluid state, has been shown to be robust and efficient when applied to compressible
multi-medium flows. Other feasible definitions of the ghost fluid state, however,
have yet to be systematically presented. By analyzing all possible wave structures
and relations for a multi-medium Riemann problem, we derive all the conditions to define
the ghost fluid state. Under these conditions, the solution in the real fluid region
can be obtained exactly, regardless of the wave pattern in the ghost fluid region. According
to the analysis herein, a practical ghost fluid method (PGFM) is proposed to
simulate compressible multi-medium flows. In contrast with the MGFM where three
degrees of freedom at the interface are required to define the ghost fluid state, only one
degree of freedom is required in this treatment. However, when these methods proved
correct in theory are used in computations for the multi-medium Riemann problem,
numerical errors at the material interface may be inevitable. We show that these errors
are mainly induced by the single-medium numerical scheme in essence, rather than
the ghost fluid method itself. Equipped with some density-correction techniques, the
PGFM is found to be able to suppress these unphysical solutions dramatically. 相似文献
5.
A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions 下载免费PDF全文
Zhenzhen Li Xijun Yu Jiang Zhu & Zupeng Jia 《Communications In Computational Physics》2014,15(4):1184-1206
This paper presents a new Lagrangian type scheme for solving the Euler
equations of compressible gas dynamics. In this new scheme the system of equations
is discretized by Runge-Kutta Discontinuous Galerkin (RKDG) method, and the mesh
moves with the fluid flow. The scheme is conservative for the mass, momentum and
total energy and maintains second-order accuracy. The scheme avoids solving the geometrical
part and has free parameters. Results of some numerical tests are presented
to demonstrate the accuracy and the non-oscillatory property of the scheme. 相似文献
6.
Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations 下载免费PDF全文
The adaptive generalized Riemann problem (GRP) scheme for 2-D compressible
fluid flows has been proposed in [J. Comput. Phys., 229 (2010), 1448–1466]
and it displays the capability in overcoming difficulties such as the start-up error for
a single shock, and the numerical instability of the almost stationary shock. In this
paper, we will provide the accuracy study and particularly show the performance in
simulating 2-D complex wave configurations formulated with the 2-D Riemann problems
for compressible Euler equations. For this purpose, we will first review the GRP
scheme briefly when combined with the adaptive moving mesh technique and consider
the accuracy of the adaptive GRP scheme via the comparison with the explicit
formulae of analytic solutions of planar rarefaction waves, planar shock waves, the
collapse problem of a wedge-shaped dam and the spiral formation problem. Then we
simulate the full set of wave configurations in the 2-D four-wave Riemann problems
for compressible Euler equations [SIAM J. Math. Anal., 21 (1990), 593–630], including
the interactions of strong shocks (shock reflections), vortex-vortex and shock-vortex
etc. This study combines the theoretical results with the numerical simulations, and
thus demonstrates what Ami Harten observed "for computational scientists there are two
kinds of truth: the truth that you prove, and the truth you see when you compute" [J. Sci.
Comput., 31 (2007), 185–193]. 相似文献
7.
The commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase
variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two
components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28],
to ensure conservation of mass and momentum for the fluid mixture in addition to
conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in
the mixture are not equal, making it a compressible model subject to an internal constraint. In one formulation of the compressible models with internal constraints (model
2), energy dissipation can be clearly established. An efficient numerical method is then
devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out
using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively
in the situation where the interfacial mixing layer is thin; and (b) predictions differ
significantly in binary fluid mixtures undergoing mixing with a large mixing zone.
The numerical study delineates the limitation of the commonly used incompressible
phase field model using volume fractions and thereby cautions its predictive value in
simulating well-mixed binary fluids. 相似文献
8.
A conservative modification to the ghost fluid method (GFM) is developed
for compressible multiphase flows. The motivation is to eliminate or reduce the conservation
error of the GFM without affecting its performance. We track the conservative
variables near the material interface and use this information to modify the numerical
solution for an interfacing cell when the interface has passed the cell. The modification
procedure can be used on the GFM with any base schemes. In this paper we use the
fifth order finite difference WENO scheme for the spatial discretization and the third
order TVD Runge-Kutta method for the time discretization. The level set method is
used to capture the interface. Numerical experiments show that the method is at least
mass and momentum conservative and is in general comparable in numerical resolution
with the original GFM. 相似文献
9.
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
10.
An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations 下载免费PDF全文
The computation of compressible flows becomes more challenging when the
Mach number has different orders of magnitude. When the Mach number is of order
one, modern shock capturing methods are able to capture shocks and other complex
structures with high numerical resolutions. However, if the Mach number is small, the
acoustic waves lead to stiffness in time and excessively large numerical viscosity, thus
demanding much smaller time step and mesh size than normally needed for incompressible flow simulation. In this paper, we develop an all-speed asymptotic preserving (AP) numerical scheme for the compressible isentropic Euler and Navier-Stokes
equations that is uniformly stable and accurate for all Mach numbers. Our idea is to
split the system into two parts: one involves a slow, nonlinear and conservative hyperbolic system adequate for the use of modern shock capturing methods and the other a
linear hyperbolic system which contains the stiff acoustic dynamics, to be solved implicitly. This implicit part is reformulated into a standard pressure Poisson projection
system and thus possesses sufficient structure for efficient fast Fourier transform solution techniques. In the zero Mach number limit, the scheme automatically becomes a
projection method-like incompressible solver. We present numerical results in one and
two dimensions in both compressible and incompressible regimes. 相似文献
11.
Deep Ray Praveen Chandrashekar Ulrik S. Fjordholm & Siddhartha Mishra 《Communications In Computational Physics》2016,19(5):1111-1140
We propose an entropy stable high-resolution finite volume scheme to approximate
systems of two-dimensional symmetrizable conservation laws on unstructured
grids. In particular we consider Euler equations governing compressible flows.
The scheme is constructed using a combination of entropy conservative fluxes and
entropy-stable numerical dissipation operators. High resolution is achieved based on
a linear reconstruction procedure satisfying a suitable sign property that helps to maintain
entropy stability. The proposed scheme is demonstrated to robustly approximate
complex flow features by a series of benchmark numerical experiments. 相似文献
12.
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
13.
A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows 下载免费PDF全文
Xueying Zhang Haiyan Tian Leihsin Kuo & Wen Chen 《Communications In Computational Physics》2013,14(2):425-442
In this paper, we study a class of contact smoothed particle hydrodynamics
(SPH) by introducing Riemann solvers and using high-order limiters. In particular, a
promising concept of WENO interpolation as limiter is presented in the reconstruction
process. The physical values relating interactional particles used as the initial values of
the Riemann problem can be reconstructed by the Taylor series expansion. The contact
solvers of the Riemann problem at contact points are incorporated in SPH approximations. In order to keep the fluid density at the wall rows to be consistent with that of
the inner fluid wall boundaries, several lines of dummy particles are placed outside
of the solid walls, which are assigned according to the initial configuration. At last,
the method is applied to compressible flows with sharp discontinuities such as the
collision of two strong shocks and the interaction of two blast waves and so on. The
numerical results indicate that the method is capable of handling sharp discontinuity
and efficiently reducing unphysical oscillations. 相似文献
14.
Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes 下载免费PDF全文
In this article we present a new class of high order accurate ArbitraryEulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high
order accuracy in space and a high order one-step time discretization is achieved by
using the local space-time Galerkin predictor proposed in [25]. For that purpose, a
new element-local weak formulation of the governing PDE is adopted on moving
space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes.
Moreover, a polynomial mapping defined by the same local space-time basis functions
as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the
final ALE one-step finite volume scheme uses moving triangular meshes with straight
edges. This is possible in the ALE framework, which allows a local mesh velocity that
is different from the local fluid velocity. We present numerical convergence rates for
the schemes presented in this paper up to sixth order of accuracy in space and time and
show some classical numerical test problems for the two-dimensional Euler equations
of compressible gas dynamics. 相似文献
15.
Wenhua Ma Dongmi Luo Wenjun Ying Guoxi Ni Min Xiao & Yibing Chen 《Communications In Computational Physics》2023,33(3):849-883
For compressible reactive flows with stiff source terms, a new block-based
adaptive multi-resolution method coupled with the adaptive multi-resolution representation model for ZND detonation and a conservative front capturing method based
on a level-set technique is presented. When simulating stiff reactive flows, underresolution in space and time can lead to incorrect propagation speeds of discontinuities, and numerical dissipation makes it impossible for traditional shock-capturing
methods to locate the detonation front. To solve these challenges, the proposed method
leverages an adaptive multi-resolution representation model to separate the scales of
the reaction from those of fluid dynamics, achieving both high-resolution solutions
and high efficiency. A level set technique is used to capture the detonation front
sharply and reduce errors due to the inaccurate prediction of detonation speed. In
order to ensure conservation, a conservative modified finite volume scheme is implemented, and the front transition fluxes are calculated by considering a Riemann problem. A series of numerical examples of stiff detonation simulations are performed to
illustrate that the present method can acquire the correct propagation speed and accurately capture the sharp detonation front. Comparative numerical results also validate
the approach’s benefits and excellent performance. 相似文献
16.
Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shock-capturing in compressible fluid flow and
avoid excessive damping of fine-scale flow features such as turbulence. Under certain conditions in compressible turbulence, however, numerical dissipation remains
unacceptably high even after optimization of the linear component that dominates
in smooth regions. Of the nonlinear error that remains, we demonstrate that a large
fraction is generated by a "synchronization deficiency" that interferes with the expression of theoretically predicted numerical performance characteristics when the WENO
adaptation mechanism is engaged. This deficiency is illustrated numerically in simulations of a linearly advected sinusoidal wave and the Shu-Osher problem [J. Comput. Phys., 83 (1989), pp. 32-78]. It is shown that attempting to correct this deficiency
through forcible synchronization results in violation of conservation. We conclude
that, for the given choice of candidate stencils, the synchronization deficiency cannot
be adequately resolved under the current WENO smoothness measurement technique. 相似文献
17.
Keiichi Kitamura Eiji Shima Keiichiro Fujimoto & Z. J. Wang 《Communications In Computational Physics》2011,10(1):90-119
In low speed flow computations, compressible finite-volume solvers are
known to a) fail to converge in acceptable time and b) reach unphysical solutions.
These problems are known to be cured by A) preconditioning on the time-derivative
term, and B) control of numerical dissipation, respectively. There have been several
methods of A) and B) proposed separately. However, it is unclear which combination
is the most accurate, robust, and efficient for low speed flows. We carried out a
comparative study of several well-known or recently-developed low-dissipation Euler
fluxes coupled with a preconditioned LU-SGS (Lower-Upper Symmetric Gauss-Seidel)
implicit time integration scheme to compute steady flows. Through a series of numerical
experiments, accurate, efficient, and robust methods are suggested for low speed
flow computations. 相似文献
18.
Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers 下载免费PDF全文
Helen C. Yee Bjorn Sjö green & Abdellah Hadjadj 《Communications In Computational Physics》2012,12(5):1603-1622
Three high order shock-capturing schemes are compared for large eddy
simulations (LES) of temporally evolving mixing layers for different convective Mach
numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5),
seventh-order WENO (WENO7) and the associated eighth-order central spatial base
scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter
step (WENO7fi). This high order nonlinear filter method of Yee & Sjogreen is designed for accurate and efficient simulations of shock-free compressible turbulence,
turbulence with shocklets and turbulence with strong shocks with minimum tuning
of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published
direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar,
whereas results by WENO5 and WENO7 compare poorly with experimental data and
DNS computations. 相似文献
19.
A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems 下载免费PDF全文
Zhuang Zhao Yong-Tao Zhang Yibing Chen & Jianxian Qiu 《Communications In Computational Physics》2021,30(3):851-873
In this paper, we develop a novel approach by combining a new robust finite difference Hermite weighted essentially non-oscillatory (HWENO) method [51]
with the modified ghost fluid method (MGFM) [25] to simulate the compressible two-medium flow problems. The main idea is that we first use the technique of the MGFM
to transform a two-medium flow problem to two single-medium cases by defining the
ghost fluids status based on the predicted interface status. Then the efficient and robust
HWENO finite difference method is applied for solving the single-medium flow cases.
By using immediate neighbor information to deal with both the solution and its derivatives, the fifth order finite difference HWENO scheme adopted in this paper is more
compact and has higher resolution than the classical fifth order finite difference WENO
scheme of Jiang and Shu [14]. Furthermore, by combining the HWENO scheme with
the MGFM to simulate the two-medium flow problems, less ghost point information
is needed than that in using the classical WENO scheme in order to obtain the same
numerical accuracy. Various one-dimensional and two-dimensional two-medium flow
problems are solved to illustrate the good performances of the proposed method. 相似文献
20.
Numerical Simulation of Compressible Vortical Flows Using a Conservative Unstructured-Grid Adaptive Scheme 下载免费PDF全文
Giuseppe Forestieri Alberto Guardone Dario Isola Filippo Marulli & Giuseppe Quaranta 《Communications In Computational Physics》2012,12(3):866-884
A two-dimensional numerical scheme for the compressible Euler equations
is presented and applied here to the simulation of exemplary compressible vortical
flows. The proposed approach allows to perform computations on unstructured moving grids with adaptation, which is required to capture complex features of the flow-field. Grid adaptation is driven by suitable error indicators based on the Mach number
and by element-quality constraints as well. At the new time level, the computational
grid is obtained by a suitable combination of grid smoothing, edge-swapping, grid
refinement and de-refinement. The grid modifications—including topology modification due to edge-swapping or the insertion/deletion of a new grid node—are interpreted at the flow solver level as continuous (in time) deformations of suitably-defined
node-centered finite volumes. The solution over the new grid is obtained without explicitly resorting to interpolation techniques, since the definition of suitable interface
velocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Numerical simulations
of the steady oblique-shock problem, of the steady transonic flow and of the start-up
unsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately. 相似文献