共查询到20条相似文献,搜索用时 31 毫秒
1.
Bao Zhu Jiefu Chen Wanxie Zhong & Qing Huo Liu 《Communications In Computational Physics》2011,9(3):828-842
A quasi non-overlapping hybrid scheme that combines the finite-difference
time-domain (FDTD) method and the finite-element time-domain (FETD) method with
nonconforming meshes is developed for time-domain solutions of Maxwell's equations.
The FETD method uses mixed-order basis functions for electric and magnetic
fields, while the FDTD method uses the traditional Yee's grid; the two methods are
joined by a buffer zone with the FETD method and the discontinuous Galerkin method
is used for the domain decomposition in the FETD subdomains. The main features of
this technique is that it allows non-conforming meshes and an arbitrary numbers of
FETD and FDTD subdomains. The hybrid method is completely stable for the time
steps up to the stability limit for the FDTD method and FETD method. Numerical
results demonstrate the validity of this technique. 相似文献
2.
A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space
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Darae Jeong Yibao Li Chaeyoung Lee Junxiang Yang & Junseok Kim 《Communications In Computational Physics》2020,27(2):412-430
In this paper, we develop a conservative numerical method for the Cahn–
Hilliard equation with generalized mobilities on curved surfaces in three-dimensional
space. We use an unconditionally gradient stable nonlinear splitting numerical scheme
and solve the resulting system of implicit discrete equations on a discrete narrow band
domain by using a Jacobi-type iteration. For the domain boundary cells, we use the
trilinear interpolation using the closest point method. The proposing numerical algorithm is computationally efficient because we can use the standard finite difference
Laplacian scheme on three-dimensional Cartesian narrow band mesh instead of discrete Laplace–Beltrami operator on triangulated curved surfaces. In particular, we employ a mass conserving correction scheme, which enforces conservation of total mass.
We perform numerical experiments on the various curved surfaces such as sphere,
torus, bunny, cube, and cylinder to demonstrate the performance and effectiveness of
the proposed method. We also present the dynamics of the CH equation with constant
and space-dependent mobilities on the curved surfaces. 相似文献
3.
Splitting Finite Difference Methods on Staggered Grids for the Three-Dimensional Time-Dependent Maxwell Equations
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In this paper, we study splitting numerical methods for the three-dimensional
Maxwell equations in the time domain. We propose a new kind of splitting finite-difference time-domain schemes on a staggered grid, which consists of only two stages
for each time step. It is proved by the energy method that the splitting scheme is unconditionally stable and convergent for problems with perfectly conducting boundary
conditions. Both numerical dispersion analysis and numerical experiments are also
presented to illustrate the efficiency of the proposed schemes. 相似文献
4.
We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the
solution of the shallow water equations (SWE) with the bottom topography as a source
term. Our new scheme will be based on the FVEG methods presented in (Noelle and
Kraft, J. Comp. Phys., 221 (2007)), but adds the possibility to handle dry boundaries.
The most important aspect is to preserve the positivity of the water height. We present
a general approach to ensure this for arbitrary finite volume schemes. The main idea is
to limit the outgoing fluxes of a cell whenever they would create negative water height.
Physically, this corresponds to the absence of fluxes in the presence of vacuum. Well-balancing
is then re-established by splitting gravitational and gravity driven parts of
the flux. Moreover, a new entropy fix is introduced that improves the reproduction of
sonic rarefaction waves. 相似文献
5.
Simulation of Plasma Flow Injection with Multi-Hierarchy Model Aiming Magnetic Reconnection Studies
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S. Usami H. Ohtani R. Horiuchi & M. Den 《Communications In Computational Physics》2012,11(3):1006-1021
A multi-hierarchy simulation model aiming magnetic reconnection studies is developed and improved in which macroscopic and microscopic physics are computed consistently and simultaneously. Macroscopic physics is solved by magnetohydrodynamics (MHD) algorithm, while microscopic dynamics is expressed by particle-in-cell (PIC) algorithm. The multi-hierarchy model relies on the domain decomposition method, and macro- and micro-hierarchies are interlocked smoothly by hand-shake scheme. As examination, plasma flow injection is simulated in the multi-hierarchy model. It is observed that plasmas flow from a macro-hierarchy to a micro-hierarchy across the magnetic field smoothly and continuously. 相似文献
6.
Craig Collins Jie Shen & Steven M. Wise 《Communications In Computational Physics》2013,13(4):929-957
We present an unconditionally energy stable and uniquely solvable finite
difference scheme for the Cahn-Hilliard-Brinkman (CHB) system, which is comprised
of a Cahn-Hilliard-type diffusion equation and a generalized Brinkman equation modeling fluid flow. The CHB system is a generalization of the Cahn-Hilliard-Stokes model
and describes two phase very viscous flows in porous media. The scheme is based on
a convex splitting of the discrete CH energy and is semi-implicit. The equations at the
implicit time level are nonlinear, but we prove that they represent the gradient of a
strictly convex functional and are therefore uniquely solvable, regardless of time step
size. Owing to energy stability, we show that the scheme is stable in the time and space
discrete$ℓ^∞$(0,$T$;$H^1_h$) and $ℓ^2$(0,$T$;$H^2_h$) norms. We also present an efficient, practical nonlinear multigrid method – comprised of a standard FAS method for the Cahn-Hilliard
part, and a method based on the Vanka smoothing strategy for the Brinkman part – for
solving these equations. In particular, we provide evidence that the solver has nearly
optimal complexity in typical situations. The solver is applied to simulate spinodal
decomposition of a viscous fluid in a porous medium, as well as to the more general
problems of buoyancy- and boundary-driven flows. 相似文献
7.
Linghua Kong Jialin Hong & Jingjing Zhang 《Communications In Computational Physics》2013,14(1):219-241
The local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis. 相似文献
8.
A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes
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Yunlong Yu Yanzhong Yao Guangwei Yuan & Xingding Chen 《Communications In Computational Physics》2016,20(5):1405-1423
In this paper, a conservative parallel iteration scheme is constructed to solve
nonlinear diffusion equations on unstructured polygonal meshes. The design is based
on two main ingredients: the first is that the parallelized domain decomposition is
embedded into the nonlinear iteration; the second is that prediction and correction
steps are applied at subdomain interfaces in the parallelized domain decomposition
method. A new prediction approach is proposed to obtain an efficient conservative
parallel finite volume scheme. The numerical experiments show that our parallel
scheme is second-order accurate, unconditionally stable, conservative and has linear
parallel speed-up. 相似文献
9.
A Hybrid Finite Element-Laplace Transform Method for the Analysis of Transient Electromagnetic Scattering by an Over-Filled Cavity in the Ground Plane
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Junqi Huang Aihua W. Wood & Michael J. Havrilla 《Communications In Computational Physics》2009,5(1):126-141
A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity
embedded in the infinite ground plane. The algorithm divides the whole scattering
domain into two, interior and exterior, sub-domains. In the interior sub-domain which
covers the cavity, the problem is solved via the finite element method. The problem is
solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane. The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains. The
analytical link guides the selection of the overlapping zone and eliminates the need
to use the conventional Schwartz iteration. This dramatically improves the efficiency
for solving transient scattering problems. Numerical solutions are tested favorably
against analytical ones for a canonical geometry. The perfect link over the artificial
boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method. An error analysis
is also performed. 相似文献
10.
Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
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Praveen Chandrashekar 《Communications In Computational Physics》2013,14(5):1252-1286
Centered numerical fluxes can be constructed for compressible Euler equations
which preserve kinetic energy in the semi-discrete finite volume scheme. The essential
feature is that the momentum flux should be of the form where are any consistent approximations to the
pressure and the mass flux. This scheme thus leaves most terms in the numerical
flux unspecified and various authors have used simple averaging. Here we enforce
approximate or exact entropy consistency which leads to a unique choice of all the
terms in the numerical fluxes. As a consequence, a novel entropy conservative flux that
also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed.
These fluxes are centered and some dissipation has to be added if shocks are
present or if the mesh is coarse. We construct scalar artificial dissipation terms which
are kinetic energy stable and satisfy approximate/exact entropy condition. Secondly,
we use entropy-variable based matrix dissipation flux which leads to kinetic energy
and entropy stable schemes. These schemes are shown to be free of entropy violating
solutions unlike the original Roe scheme. For hypersonic flows a blended scheme is
proposed which gives carbuncle free solutions for blunt body flows. Numerical results
for Euler and Navier-Stokes equations are presented to demonstrate the performance
of the different schemes. 相似文献
11.
Georgij Bispen K. R. Arun Má ria Luká čová -Medvid'ová & Sebastian Noelle 《Communications In Computational Physics》2014,16(2):307-347
We present new large time step methods for the shallow water flows in the
low Froude number limit. In order to take into account multiscale phenomena that typically
appear in geophysical flows nonlinear fluxes are split into a linear part governing
the gravitational waves and the nonlinear advection. We propose to approximate fast
linear waves implicitly in time and in space by means of a genuinely multidimensional
evolution operator. On the other hand, we approximate nonlinear advection part explicitly
in time and in space by means of the method of characteristics or some standard
numerical flux function. Time integration is realized by the implicit-explicit (IMEX)
method. We apply the IMEX Euler scheme, two step Runge Kutta Cranck Nicolson
scheme, as well as the semi-implicit BDF scheme and prove their asymptotic preserving
property in the low Froude number limit. Numerical experiments demonstrate
stability, accuracy and robustness of these new large time step finite volume schemes
with respect to small Froude number. 相似文献
12.
John C. Morrison Kyle Steffen Blake Pantoja Asha Nagaiya Jacek Kobus & Thomas Ericsson 《Communications In Computational Physics》2016,19(3):632-647
In order to solve the partial differential equations that arise in the Hartree-Fock
theory for diatomic molecules and in molecular theories that include electron correlation,
one needs efficient methods for solving partial differential equations. In this
article, we present numerical results for a two-variable model problem of the kind that
arises when one solves the Hartree-Fock equations for a diatomic molecule. We compare
results obtained using the spline collocation and domain decomposition methods
with third-order Hermite splines to results obtained using the more-established finite
difference approximation and the successive over-relaxation method. The theory of
domain decomposition presented earlier is extended to treat regions that are divided
into an arbitrary number of subregions by families of lines parallel to the two coordinate
axes. While the domain decomposition method and the finite difference approach
both yield results at the micro-Hartree level, the finite difference approach with a 9-point difference formula produces the same level of accuracy with fewer points. The
domain decomposition method has the strength that it can be applied to problems with
a large number of grid points. The time required to solve a partial differential equation
for a fine grid with a large number of points goes down as the number of partitions
increases. The reason for this is that the length of time necessary for solving a set of
linear equations in each subregion is very much dependent upon the number of equations.
Even though a finer partition of the region has more subregions, the time for
solving the set of linear equations in each subregion is very much smaller. This feature
of the theory may well prove to be a decisive factor for solving the two-electron pair
equation, which – for a diatomic molecule – involves solving partial differential equations
with five independent variables. The domain decomposition theory also makes
it possible to study complex molecules by dividing them into smaller fragments thatare calculated independently. Since the domain decomposition approach makes it possible
to decompose the variable space into separate regions in which the equations are
solved independently, this approach is well-suited to parallel computing. 相似文献
13.
A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation
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Wei Leng & Lili Ju 《Communications In Computational Physics》2021,29(2):357-395
In this paper, we propose and test a novel diagonal sweeping domain
decomposition method (DDM) with source transfer for solving the high-frequency
Helmholtz equation in$\mathbb{R}^n$. In the method the computational domain is partitioned into
overlapping checkerboard subdomains for source transfer with the perfectly matched
layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially
designed to solve the system efficiently. The method improves the additive overlapping DDM [43] and the L-sweeps method [50] by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global
PML problem with $2^n$ sweeps in the constant medium case. Although the sweeping
usually implies sequential subdomain solves, the number of sequential steps required
for each sweep in the method is only proportional to the $n$-th root of the number of
subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with
multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness
and efficiency of the proposed method. 相似文献
14.
Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes
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In [14], Maire developed a class of cell-centered Lagrangian schemes for
solving Euler equations of compressible gas dynamics in cylindrical coordinates. These
schemes use a node-based discretization of the numerical fluxes. The control volume version has several distinguished properties, including the conservation of mass,
momentum and total energy and compatibility with the geometric conservation law
(GCL). However, it also has a limitation in that it cannot preserve spherical symmetry
for one-dimensional spherical flow. An alternative is also given to use the first order
area-weighted approach which can ensure spherical symmetry, at the price of sacrificing conservation of momentum. In this paper, we apply the methodology proposed in
our recent work [8] to the first order control volume scheme of Maire in [14] to obtain
the spherical symmetry property. The modified scheme can preserve one-dimensional
spherical symmetry in a two-dimensional cylindrical geometry when computed on an
equal-angle-zoned initial grid, and meanwhile it maintains its original good properties
such as conservation and GCL. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme
in terms of symmetry, non-oscillation and robustness properties. 相似文献
15.
Within the projection schemes for the incompressible Navier-Stokes equations
(namely "pressure-correction" method), we consider the simplest method (of order
one in time) which takes into account the pressure in both steps of the splitting
scheme. For this scheme, we construct, analyze and implement a new high order compact
spatial approximation on nonstaggered grids. This approach yields a fourth order
accuracy in space with an optimal treatment of the boundary conditions (without error
on the velocity) which could be extended to more general splitting. We prove the
unconditional stability of the associated Cauchy problem via von Neumann analysis.
Then we carry out a normal mode analysis so as to obtain more precise results about
the behavior of the numerical solutions. Finally we present detailed numerical tests for
the Stokes and the Navier-Stokes equations (including the driven cavity benchmark)
to illustrate the theoretical results. 相似文献
16.
A fully discrete discontinuous Galerkin method is introduced for solving
time-dependent Maxwell's equations. Distinguished from the Runge-Kutta discontinuous Galerkin method (RKDG) and the finite element time domain method (FETD), in
our scheme, discontinuous Galerkin methods are used to discretize not only the spatial
domain but also the temporal domain. The proposed numerical scheme is proved to be
unconditionally stable, and a convergent rate $\mathcal{O}((∆t)^{r+1}+h^{k+1/2})$ is established under the $L^2$ -norm when polynomials of degree at most $r$ and $k$ are used for temporal and
spatial approximation, respectively. Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction. An ultra-convergence of order $(∆t)^{2r+1}$ in
time step is observed numerically for the numerical fluxes w.r.t. temporal variable at
the grid points. 相似文献
17.
Hua Guan Yandong Jiao Ju Liu & Yifa Tang 《Communications In Computational Physics》2009,6(3):639-654
By performing a particular spatial discretization to the nonlinear
Schrödinger equation (NLSE), we obtain a non-integrable Hamiltonian system which
can be decomposed into three integrable parts (L-L-N splitting). We integrate each part
by calculating its phase flow, and develop explicit symplectic integrators of different
orders for the original Hamiltonian by composing the phase flows. A 2nd-order reversible
constructed symplectic scheme is employed to simulate solitons motion and
invariants behavior of the NLSE. The simulation results are compared with a 3rd-order
non-symplectic implicit Runge-Kutta method, and the convergence of the formal energy
of this symplectic integrator is also verified. The numerical results indicate that
the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical
tool for solving the NLSE. 相似文献
18.
Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation
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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
19.
Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem
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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
20.
A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations
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The Douglas-Rachford and Peaceman-Rachford splitting methods are common
choices for temporal discretizations of evolution equations. In this paper we combine
these methods with spatial discretizations fulfilling some easily verifiable criteria.
In the setting of linear dissipative evolution equations we prove optimal convergence
orders, simultaneously in time and space. We apply our abstract results to dimension
splitting of a 2D diffusion problem, where a finite element method is used for spatial
discretization. To conclude, the convergence results are illustrated with numerical
experiments. 相似文献