共查询到20条相似文献,搜索用时 31 毫秒
1.
High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes 下载免费PDF全文
Weijie Zhang Yulong Xing Yinhua Xia & Yan Xu 《Communications In Computational Physics》2022,31(3):771-815
In this paper, we propose a high-order accurate discontinuous Galerkin
(DG) method for the compressible Euler equations under gravitational fields on unstructured meshes. The scheme preserves a general hydrostatic equilibrium state and
provably guarantees the positivity of density and pressure at the same time. Comparing with the work on the well-balanced scheme for Euler equations with gravitation
on rectangular meshes, the extension to triangular meshes is conceptually plausible
but highly nontrivial. We first introduce a special way to recover the equilibrium state
and then design a group of novel variables at the interface of two adjacent cells, which
plays an important role in the well-balanced and positivity-preserving properties. One
main challenge is that the well-balanced schemes may not have the weak positivity
property. In order to achieve the well-balanced and positivity-preserving properties
simultaneously while maintaining high-order accuracy, we carefully design DG spatial discretization with well-balanced numerical fluxes and suitable source term approximation. For the ideal gas, we prove that the resulting well-balanced scheme, coupled with strong stability preserving time discretizations, satisfies a weak positivity
property. A simple existing limiter can be applied to enforce the positivity-preserving
property, without losing high-order accuracy and conservation. Extensive one- and
two-dimensional numerical examples demonstrate the desired properties of the proposed scheme, as well as its high resolution and robustness. 相似文献
2.
R. Chauvin S. Guisset B. Manach-Perennou & L. Martaud 《Communications In Computational Physics》2022,31(1):293-330
A positivity-preserving, conservative and entropic numerical scheme is presented for the three-temperature grey diffusion radiation hydrodynamics model. More
precisely, the dissipation matrices of the colocalized semi-Lagrangian scheme are defined in order to enforce the entropy production on each species (electron or ion) proportionally to its mass as prescribed in [34]. A reformulation of the model is then considered to enable the derivation of a robust convex combination based scheme. This
yields the positivity-preserving property at each sub-iteration of the algorithm while
the total energy conservation is reached at convergence. Numerous pure hydrodynamics and radiation hydrodynamics test cases are carried out to assess the accuracy of the
method. The question of the stability of the scheme is also addressed. It is observed
that the present numerical method is particularly robust. 相似文献
3.
A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases 下载免费PDF全文
Assumed having axial symmetry, the streamer discharge is often described
by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation.
Without additional care for a stricter CFL condition or special treatment to the negative source term, popular methods used in streamer discharge simulations, e.g., FEM-FCT, FVM, cannot ensure the positivity of the particle densities for the cases in attaching gases. By introducing the positivity-preserving limiter proposed by Zhang and
Shu [15] and Strang operator splitting, this paper proposes a finite difference scheme
with a provable positivity-preserving property in cylindrical coordinate system, for
the numerical simulation of streamer discharges in non-attaching and attaching gases.
Numerical examples in non-attaching gas (N2) and attaching gas (SF6) are given to
illustrate the effectiveness of the scheme. 相似文献
4.
Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem 下载免费PDF全文
Jiajie Chen Xiaofeng Cai Jianxian Qiu & Jing-Mei Qiu 《Communications In Computational Physics》2021,30(1):67-96
We present a new conservative semi-Lagrangian finite difference weighted
essentially non-oscillatory scheme with adaptive order. This is an extension of the
conservative semi-Lagrangian (SL) finite difference WENO scheme in [Qiu and Shu,
JCP, 230 (4) (2011), pp. 863-889], in which linear weights in SL WENO framework
were shown not to exist for variable coefficient problems. Hence, the order of accuracy is not optimal from reconstruction stencils. In this paper, we incorporate a recent
WENO adaptive order (AO) technique [Balsara et al., JCP, 326 (2016), pp. 780-804]
to the SL WENO framework. The new scheme can achieve an optimal high order of
accuracy, while maintaining the properties of mass conservation and non-oscillatory
capture of solutions from the original SL WENO. The positivity-preserving limiter is
further applied to ensure the positivity of solutions. Finally, the scheme is applied to
high dimensional problems by a fourth-order dimensional splitting. We demonstrate
the effectiveness of the new scheme by extensive numerical tests on linear advection
equations, the Vlasov-Poisson system, the guiding center Vlasov model as well as the
incompressible Euler equations. 相似文献
5.
Wenbin Chen Jianyu Jing Cheng Wang Xiaoming Wang & Steven M. Wise 《Communications In Computational Physics》2022,31(1):60-93
In this paper we propose and analyze a second order accurate numerical
scheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order Adams-Bashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme,
which ensures the positivity-preserving property, i.e., the numerical value of the phase
variable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special form
of the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearized
stability analysis. A few numerical results, including both the constant-mobility and
solution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme. 相似文献
6.
A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters 下载免费PDF全文
Lixiu Dong Cheng Wang Hui Zhang & Zhengru Zhang 《Communications In Computational Physics》2020,28(3):967-998
We present and analyze a new second-order finite difference scheme for
the Macromolecular Microsphere Composite hydrogel, Time-Dependent Ginzburg-Landau (MMC-TDGL) equation, a Cahn-Hilliard equation with Flory-Huggins-deGennes energy potential. This numerical scheme with unconditional energy stability is based on the Backward Differentiation Formula (BDF) method in time derivation
combining with Douglas-Dupont regularization term. In addition, we present a pointwise bound of the numerical solution for the proposed scheme in the theoretical level.
For the convergent analysis, we treat three nonlinear logarithmic terms as a whole and
deal with all logarithmic terms directly by using the property that the nonlinear error
inner product is always non-negative. Moreover, we present the detailed convergent
analysis in $ℓ^∞$(0,$T$;$H_h^{-1}$)∩$ℓ^2$(0,$T$;$H_h^1$) norm. At last, we use the local Newton approximation and multigrid method to solve the nonlinear numerical scheme, and various
numerical results are presented, including the numerical convergence test, positivity-preserving property test, spinodal decomposition, energy dissipation and mass conservation properties. 相似文献
7.
Yongping Cheng Haiyun Dong Maojun Li & Weizhi Xian 《Communications In Computational Physics》2020,28(4):1437-1463
In this paper, we focus on the numerical simulation of the two-layer shallow water equations over variable bottom topography. Although the existing numerical schemes for the single-layer shallow water equations can be extended to two-layer
shallow water equations, it is not a trivial work due to the complexity of the equations.
To achieve the well-balanced property of the numerical scheme easily, the two-layer
shallow water equations are reformulated into a new form by introducing two auxiliary variables. Since the new equations are only conditionally hyperbolic and their
eigenstructure cannot be easily obtained, we consider the utilization of the central discontinuous Galerkin method which is free of Riemann solvers. By choosing the values
of the auxiliary variables suitably, we can prove that the scheme can exactly preserve
the still-water solution, and thus it is a truly well-balanced scheme. To ensure the
non-negativity of the water depth, a positivity-preserving limiter and a special approximation to the bottom topography are employed. The accuracy and validity of the
numerical method will be illustrated through some numerical tests. 相似文献
8.
Antonio Raudino Antonio Grassi Giuseppe Lombardo Giovanni Russo Clarissa Astuto & Mario Corti 《Communications In Computational Physics》2022,31(3):707-738
In this paper we propose a computational framework for the investigation
of the correlated motion between positive and negative ions exposed to the attraction
of a bubble surface that mimics the (oscillating) cell membrane. Specifically we aim
to investigate the role of surface traps with substances freely diffusing around the cell.
The physical system we want to model is an anchored gas drop submitted to a diffusive flow of charged surfactants (ions). When the diffusing surfactants meet the surface
of the bubble, they are reversibly adsorbed and their local concentration is accurately
measured. The correlated diffusion of surfactants is described by a Poisson-Nernst-Planck (PNP) system, in which the drift term is given by the gradient of a potential
which includes both the effect of the bubble and the Coulomb interaction between
the carriers. The latter term is obtained from the solution of a self-consistent Poisson
equation. For very short Debye lengths one can adopt the so called Quasi-Neutral
limit which drastically simplifies the system, thus allowing for much faster numerical
simulations. The paper has four main objectives. The first one is to present a PNP
model that describes ion charges in presence of a trap. The second one is to provide
benchmark tests for the validation of simplified multiscale models under current development [1]. The third one is to explore the relevance of the term describing the
interaction among the apolar tails of the anions. The last one is to quantitatively explore the validity of the Quasi-Neutral limit by comparison with detailed numerical
simulation for smaller and smaller Debye lengths. In order to reach these goals, we
propose a simple and efficient Alternate Direction Implicit method for the numerical
solution of the non-linear PNP system, which guarantees second order accuracy bothin space and time, without requiring solution of nonlinear equation at each time step.
New semi-implicit scheme for a simplified PNP system near quasi neutrality is also
proposed. 相似文献
9.
Two Nonlinear Positivity-Preserving Finite Volume Schemes for Three-Dimensional Heat Conduction Equations on General Polyhedral Meshes 下载免费PDF全文
Menghuan Liu Shi Shu Guangwei Yuan & Xiaoqiang Yue 《Communications In Computational Physics》2021,30(4):1185-1215
In this article we present two types of nonlinear positivity-preserving finite
volume (PPFV) schemes for a class of three-dimensional heat conduction equations on
general polyhedral meshes. First, we present a new parameter selection strategy on the
one-sided flux and establish a nonlinear PPFV scheme based on a two-point flux with
higher efficiency. By comparing with the scheme proposed in [H. Xie, X. Xu, C. Zhai,
H. Yong, Commun. Comput. Phys. 24 (2018) 1375–1408], our scheme avoids the assumption that the values of auxiliary unknowns are nonnegative, which makes our
interpolation formulae suitable to be constructed by existing approaches with high
accuracy and well robustness (e.g., the finite element method), thus enhancing the
adaptability to distorted meshes with large deformations. Then we derive a linear
multi-point flux involving combination coefficients and, via the Patankar trick, obtain
another nonlinear PPFV scheme that is concise and easy to implement. The selection
strategy of combination coefficients is also provided to improve the convergence behavior of the Picard procedure. Furthermore, the existence and positivity-preserving
properties of these two nonlinear PPFV solutions are proved. Numerical experiments
with the discontinuous diffusion scalar as well as discontinuous and anisotropic diffusion tensors are given to confirm our theoretical findings and demonstrate that our
schemes both can achieve ideal-order accuracy even on severely distorted meshes. 相似文献
10.
A Decoupled and Positivity-Preserving DDFVS Scheme for Diffusion Problems on Polyhedral Meshes 下载免费PDF全文
We propose a decoupled and positivity-preserving discrete duality finite
volume (DDFV) scheme for anisotropic diffusion problems on polyhedral meshes with
star-shaped cells and planar faces. Under the generalized DDFV framework, two sets
of finite volume (FV) equations are respectively constructed on the dual and primary
meshes, where the ones on the dual mesh are derived from the ingenious combination
of a geometric relationship with the construction of the cell matrix. The resulting system on the dual mesh is symmetric and positive definite, while the one on the primary
mesh possesses an M-matrix structure. To guarantee the positivity of the two categories of unknowns, a cutoff technique is introduced. As for the local conservation, it
is conditionally maintained on the dual mesh while strictly preserved on the primary
mesh. More interesting is that the FV equations on the dual mesh can be solved independently, so that the two sets of FV equations are decoupled. As a result, no nonlinear
iteration is required for linear problems and a general nonlinear solver could be used
for nonlinear problems. In addition, we analyze the well-posedness of numerical solutions for linear problems. The properties of the presented scheme are examined by
numerical experiments. The efficiency of the Newton method is also demonstrated by
comparison with those of the fixed-point iteration method and its Anderson acceleration. 相似文献
11.
Jian-Guo Liu Jinhuan Wang Yu Zhao & Zhennan Zhou 《Communications In Computational Physics》2021,30(3):874-902
In this paper, we consider the field model for complex ionic fluids with an
energy variational structure, and analyze the well-posedness to this model with regularized kernels. Furthermore, we deduce the estimate of the maximal density function to quantify the finite size effect. On the numerical side, we adopt a finite volume scheme to the field model, which satisfies the following properties: positivity-preserving, mass conservation and energy dissipation. Besides, series of numerical experiments are provided to demonstrate the properties of the steady state and the finite
size effect by showing the equilibrium profiles with different values of the parameter
in the kernel. 相似文献
12.
A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations 下载免费PDF全文
A high-order, well-balanced, positivity-preserving quasi-Lagrange moving
mesh DG method is presented for the shallow water equations with non-flat bottom
topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or
tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving
mesh DG method, a hydrostatic reconstruction technique, and a change of unknown
variables. The strategies in the use of slope limiting, positivity-preservation limiting,
and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats
mesh movement continuously in time and has the advantages that it does not need to
interpolate flow variables from the old mesh to the new one and places no constraint
for the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and
its ability to adapt the mesh according to features in the flow and bottom topography. 相似文献
13.
Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment 下载免费PDF全文
Da Meng Bin Zheng Guang Lin & Maria L. Sushko 《Communications In Computational Physics》2014,16(5):1298-1322
We have developed efficient numerical algorithms for solving 3D steady-state
Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described
by the classical density functional theory (cDFT). The coupled PNP equations are discretized
by a finite difference scheme and solved iteratively using the Gummel method
with relaxation. The Nernst-Planck equations are transformed into Laplace equations
through the Slotboom transformation. Then, the algebraic multigrid method is
applied to efficiently solve the Poisson equation and the transformed Nernst-Planck
equations. A novel strategy for calculating excess chemical potentials through fast
Fourier transforms is proposed, which reduces computational complexity from $\mathcal{O}$($N^2$) to $\mathcal{O}$($NlogN$), where $N$ is the number of grid points. Integrals involving the Dirac
delta function are evaluated directly by coordinate transformation, which yields more
accurate results compared to applying numerical quadrature to an approximated delta
function. Numerical results for ion and electron transport in solid electrolyte for lithium-ion
(Li-ion) batteries are shown to be in good agreement with the experimental data
and the results from previous studies. 相似文献
14.
An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes 下载免费PDF全文
This paper develops an efficient positivity-preserving finite volume scheme
for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh,
while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed
stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically,
our scheme does not require any nonlinear iteration for the linear problems, and can
call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The
positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the
accuracy, efficiency and positivity of the scheme on various distorted meshes. 相似文献
15.
16.
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
17.
An Implicit Scheme for Moving Walls and Multi-Material Interfaces in Weakly Compressible Materials 下载免费PDF全文
Emanuela Abbate Angelo Iollo & Gabriella Puppo 《Communications In Computational Physics》2020,27(1):116-144
We propose a numerical method for the simulation of flows from weakly
compressible to low Mach regimes in domains with moving boundaries. Non-miscible
weakly compressible materials separated by an interface are included as well. The
scheme is fully implicit and it exploits the relaxation all-speed scheme introduced
in [1]. We consider media with significantly different physical properties and constitutive laws, as fluids and hyperelastic solids. The proposed numerical scheme is
fully Eulerian and it is the same for all materials. We present numerical validations by
simulating weakly compressible fluid/fluid, solid/solid and solid/fluid interactions. 相似文献
18.
Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations 下载免费PDF全文
We consider in this paper random batch interacting particle methods for
solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann
(PB) equation as the equilibrium, in the external unbounded domain. To justify the
simulation in a truncated domain, an error estimate of the truncation is proved in
the symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are $\mathcal{O}(N)$ per time step. The particle methods can
not only be considered as a numerical method for solving the PNP and PB equations,
but also can be used as a direct simulation approach for the dynamics of the charged
particles in solution. The particle methods are preferable due to their simplicity and
adaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effects
and interactions in the particle methods and to describe phenomena beyond the scope
of the mean-field equations. 相似文献
19.
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
20.
Jiwei Zhang Zhizhong Sun Xiaonan Wu & Desheng Wang 《Communications In Computational Physics》2011,10(3):742-766
The paper is concerned with the numerical solution of Schrödinger equations
on an unbounded spatial domain. High-order absorbing boundary conditions
for one-dimensional domain are derived, and the stability of the reduced initial boundary
value problem in the computational interval is proved by energy estimate. Then a
second order finite difference scheme is proposed, and the convergence of the scheme
is established as well. Finally, numerical examples are reported to confirm our error
estimates of the numerical methods. 相似文献