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1.
A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations
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Laiping Zhang Wei Liu Lixin He & Xiaogang Deng 《Communications In Computational Physics》2012,12(1):284-314
A concept of "static reconstruction" and "dynamic reconstruction" was introduced for higher-order (third-order or more) numerical methods in our previous
work. Based on this concept, a class of hybrid DG/FV methods had been developed
for one-dimensional conservation law using a "hybrid reconstruction" approach, and
extended to two-dimensional scalar equations on triangular and Cartesian/triangular
hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called
as "dynamic reconstruction"), while the higher-order derivatives are reconstructed by
the "static reconstruction" of the FV method, using the known lower-order derivatives
in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV
schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate
the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction,
subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic
flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV
method achieves the desired third-order accuracy, and the applications demonstrate
that they can capture the flow structure accurately, and can reduce the CPU time and
memory requirement greatly than the traditional DG method with the same order of
accuracy. 相似文献
2.
Shuai Shao Ming Li Nianhua Wang & Laiping Zhang 《Communications In Computational Physics》2020,27(3):725-752
A new hybrid reconstruction scheme DDG/FV is developed in this work
by combining the DDG method and DG/FV hybrid scheme developed in the authors' previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L2 projection and the least-squares method
are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L2 projection based on orthogonal basis functions
is implemented to improve the efficiency of reconstruction. Three typical test cases,
including the 3D Couette flow, laminar flows over an analytical 3D body of revolution
and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV
method. The numerical results demonstrate that the DDG scheme can accelerate the
convergence history compared with widely-used BR2 scheme. More attractively, the
new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with
more than 2 times of efficiency improvement in solving 3D Navier-Stokes equations on
tetrahedral grids, and even one-order of magnitude faster in some cases, which shows
good potential in future realistic applications. 相似文献
3.
An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids
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Takanori Haga Keisuke Sawada & Z. J. Wang 《Communications In Computational Physics》2009,6(5):978-996
An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solution
approach has been applied to a high order spectral volume (SV) method for unstructured
tetrahedral grids. The LU-SGS solver is preconditioned by the block element
matrix, and the system of equations is then solved with a LU decomposition.
The compact feature of SV reconstruction facilitates the efficient solution algorithm
even for high order discretizations. The developed implicit solver has shown more
than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme
for typical inviscid and viscous problems. A convergence to a high order solution for
high Reynolds number transonic flow over a 3D wing with a one equation turbulence
model is also indicated. 相似文献
4.
A Comparative Study of Rosenbrock-Type and Implicit Runge-Kutta Time Integration for Discontinuous Galerkin Method for Unsteady 3D Compressible Navier-Stokes equations
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Xiaodong Liu Yidong Xia Hong Luo & Lijun Xuan 《Communications In Computational Physics》2016,20(4):1016-1044
A comparative study of two classes of third-order implicit time integration
schemes is presented for a third-order hierarchical WENO reconstructed discontinuous
Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes
equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3)
scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential
algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme,
a remarkable feature of the ROW schemes is that, they only require one approximate
Jacobian matrix calculation every time step, thus considerably reducing the overall
computational cost. A variety of test cases, ranging from inviscid flows to DNS of
turbulent flows, are presented to assess the performance of these schemes. Numerical
experiments demonstrate that the third-order ROW scheme for the DAEs of index-2
can not only achieve the designed formal order of temporal convergence accuracy in
a benchmark test, but also require significantly less computing time than its ESDIRK3
counterpart to converge to the same level of discretization errors in all of the flow
simulations in this study, indicating that the ROW methods provide an attractive alternative
for the higher-order time-accurate integration of the unsteady compressible
Navier-Stokes equations. 相似文献
5.
Adaptive Fully Implicit Simulator with Multilevel Schwarz Methods for Gas Reservoir Flows in Fractured Porous Media
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Large-scale reservoir modeling and simulation of gas reservoir flows in fractured porous media is currently an important topic of interest in petroleum engineering. In this paper, the dual-porosity dual-permeability (DPDP) model coupled with
the Peng-Robinson equation of state (PR-EoS) is used for the mathematical model of
the gas reservoir flow in fractured porous media. We develop and study a parallel and
highly scalable reservoir simulator based on an adaptive fully implicit scheme and
an inexact Newton type method to solve this dual-continuum mathematical model.
In the approach, an explicit-first-step, single-diagonal-coefficient, diagonally implicit
Runge–Kutta (ESDIRK) method with adaptive time stepping is proposed for the fully
implicit discretization, which is second-order and L-stable. And then we focus on the
family of Newton–Krylov methods for the solution of a large sparse nonlinear system
of equations arising at each time step. To accelerate the convergence and improve the
scalability of the solver, a class of multilevel monolithic additive Schwarz methods is
employed for preconditioning. Numerical results on a set of ideal as well as realistic
flow problems are used to demonstrate the efficiency and the robustness of the proposed methods. Experiments on a supercomputer with several thousand processors
are also carried out to show that the proposed reservoir simulator is highly scalable. 相似文献
6.
A Decoupled and Positivity-Preserving DDFVS Scheme for Diffusion Problems on Polyhedral Meshes
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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
7.
Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation
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Rongpei Zhang Xijun Yu Jiang Zhu Abimael F. D. Loula & Xia Cui 《Communications In Computational Physics》2013,14(5):1287-1303
Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semi-implicit integration factor method to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe time step limits, but also take advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation. 相似文献
8.
Alina Chertock & Yongle Liu 《Communications In Computational Physics》2020,27(2):480-502
We study the two-component Camassa-Holm (2CH) equations as a model
for the long time water wave propagation. Compared with the classical Saint-Venant
system, it has the advantage of preserving the waves amplitude and shape for a long
time. We present two different numerical methods—finite volume (FV) and hybrid
finite-volume-particle (FVP) ones. In the FV setup, we rewrite the 2CH equations in a
conservative form and numerically solve it by the central-upwind scheme, while in the
FVP method, we apply the central-upwind scheme to the density equation only while
solving the momentum and velocity equations by a deterministic particle method. Numerical examples are shown to verify the accuracy of both FV and FVP methods. The
obtained results demonstrate that the FVP method outperforms the FV method and
achieves a superior resolution thanks to a low-diffusive nature of a particle approximation. 相似文献
9.
An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
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Peimeng Yin Yunqing Huang & Hailiang Liu 《Communications In Computational Physics》2014,16(2):491-515
An iterative discontinuous Galerkin (DG) method is proposed to solve the
nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which
the solution of the nonlinear PB equation is iteratively approximated through a series
of linear PB equations, while an appropriate initial guess and a suitable iterative parameter
are selected so that the solutions of linear PB equations are monotone within
the identified solution space. For the spatial discretization we apply the direct discontinuous
Galerkin method to those linear PB equations. More precisely, we use one
initial guess when the Debye parameter λ=O(1), and a special initial guess for λ≪1
to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence,
uniqueness, and convergence of the iteration. In particular, iteration steps can
be reduced for a variable iterative parameter. Both one and two-dimensional numerical
results are carried out to demonstrate both accuracy and capacity of the iterative
DG method for both cases of λ=O(1) and λ≪1. The (m+1)th order of accuracy for
L2 and mth order of accuracy for H1for Pm elements are numerically obtained. 相似文献
10.
An Efficient Parallel/Unstructured-Multigrid Implicit Method for Simulating 3D Fluid-Structure Interaction
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X. Lv Y. Zhao X. Y. Huang G. H. Xia & X. H. Su 《Communications In Computational Physics》2008,4(2):350-377
A finite volume (FV) method for simulating 3D Fluid-Structure Interaction (FSI) is presented in this paper. The fluid flow is simulated using a parallel unstructured multigrid preconditioned implicit compressible solver, whist a 3D matrix-free implicit unstructured multigrid finite volume solver is employed for the structural dynamics. The two modules are then coupled using a so-called immersed membrane method (IMM). Large-Eddy Simulation (LES) is employed to predict turbulence. Results from several moving boundary and FSI problems are presented to validate proposed methods and demonstrate their efficiency. 相似文献
11.
On the Stability and CPU Time of the Implicit Runge-Kutta Schemes for Steady State Simulations
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Implicit time integration schemes are popular because their relaxed stability
constraints can result in better computational efficiency. For time-accurate unsteady
simulations, it has been well recognized that the inherent dispersion and dissipation
errors of implicit Runge-Kutta schemes will reduce the computational accuracy for
large time steps. Yet for steady state simulations using the time-dependent governing
equations, these errors are often overlooked because the intermediate solutions are of
less interest. Based on the model equation dy/dt = (µ+iλ)y of scalar convection diffusion
systems, this study examines the stability limits, dispersion and dissipation errors
of four diagonally implicit Runge-Kutta-type schemes on the complex (µ+iλ)∆t
plane. Through numerical experiments, it is shown that, as the time steps increase,
the A-stable implicit schemes may not always have reduced CPU time and the computations
may not always remain stable, due to the inherent dispersion and dissipation
errors of the implicit Runge-Kutta schemes. The dissipation errors may decelerate the
convergence rate, and the dispersion errors may cause large oscillations of the numerical
solutions. These errors, especially those of high wavenumber components, grow
at large time steps. They lead to difficulty in the convergence of the numerical computations,
and result in increasing CPU time or even unstable computations as the time
step increases. It is concluded that an optimal implicit time integration scheme for
steady state simulations should have high dissipation and low dispersion. 相似文献
12.
A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems
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We have introduced a fully second order IMplicit/EXplicit (IMEX) time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22,24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations. The IMEX method is applied to the incompressible flow equations in the following manner. The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes. On the other hand, an implicit strategy is employed for the non-hyperbolic terms. The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov (JFNK) method [8,29,31]. This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation. We employ a simple yet quite effective fractional step projection methodology (similar to those in [11,19,21,30]) as our preconditioner inside the JFNK solver. We present results from several test calculations. For each test, we show second order time convergence. Finally, we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner. 相似文献
13.
Two-Grid Method for Miscible Displacement Problem by Mixed Finite Element Methods and Mixed Finite Element Method of Characteristics
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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
14.
Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation
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The development of high-order schemes has been mostly concentrated on
the limiters and high-order reconstruction techniques. In this paper, the effect of the
flux functions on the performance of high-order schemes will be studied. Based on the
same WENO reconstruction, two schemes with different flux functions, i.e., the fifth-order WENO method and the WENO-Gas-Kinetic scheme (WENO-GKS), will be compared. The fifth-order finite difference WENO-SW scheme is a characteristic variable
reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms, the sixth-order central difference for viscous terms, and three stages Runge-Kutta time stepping for the time integration. On the other hand, the finite volume
WENO-GKS is a conservative variable reconstruction based method with the same
WENO reconstruction. But it evaluates a time dependent gas distribution function
along a cell interface, and updates the flow variables inside each control volume by
integrating the flux function along the boundary of the control volume in both space
and time. In order to validate the robustness and accuracy of the schemes, both methods are tested under a wide range of flow conditions: vortex propagation, Mach 3
step problem, and the cavity flow at Reynolds number 3200. Our study shows that
both WENO-SW and WENO-GKS yield quantitatively similar results and agree with
each other very well provided a sufficient grid resolution is used. With the reduction of mesh points, the WENO-GKS behaves to have less numerical dissipation and
present more accurate solutions than those from the WENO-SW in all test cases. For
the Navier-Stokes equations, since the WENO-GKS couples inviscid and viscous terms
in a single flux evaluation, and the WENO-SW uses an operator splitting technique, it
appears that the WENO-SW is more sensitive to the WENO reconstruction and boundary treatment. In terms of efficiency, the finite volume WENO-GKS is about 4 times
slower than the finite difference WENO-SW in two dimensional simulations. The current study clearly shows that besides high-order reconstruction, an accurate gas evolution model or flux function in a high-order scheme is also important in the capturing of physical solutions. In a physical flow, the transport, stress deformation, heat conduction, and viscous heating are all coupled in a single gas evolution process. Therefore,
it is preferred to develop such a scheme with multi-dimensionality, and unified treatment of inviscid and dissipative terms. A high-order scheme does prefer a high-order
gas evolution model. Even with the rapid advances of high-order reconstruction techniques, the first-order dynamics of the Riemann solution becomes the bottleneck for
the further development of high-order schemes. In order to avoid the weakness of the
low order flux function, the development of high-order schemes relies heavily on the
weak solution of the original governing equations for the update of additional degree
of freedom, such as the non-conservative gradients of flow variables, which cannot be
physically valid in discontinuous regions. 相似文献
15.
Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry
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T. V. S. Sekhar B. Hema Sundar Raju & Y. V. S. S. Sanyasiraju 《Communications In Computational Physics》2012,11(1):99-113
A higher-order compact scheme on the nine point 2-D stencil is developed
for the steady stream-function vorticity form of the incompressible Navier-Stokes (NS) equations in spherical polar coordinates, which was used earlier only for the cartesian and cylindrical geometries. The steady, incompressible, viscous and axially symmetric flow past a sphere is used as a model problem. The non-linearity in the N-S
equations is handled in a comprehensive manner avoiding complications in calculations. The scheme is combined with the multigrid method to enhance the convergence
rate. The solutions are obtained over a non-uniform grid generated using the transformation r = eξ while maintaining a uniform grid in the computational plane. The
superiority of the higher order compact scheme is clearly illustrated in comparison
with upwind scheme and defect correction technique at high Reynolds numbers by
taking a large domain. This is a pioneering effort, because for the first time, the fourth
order accurate solutions for the problem of viscous flow past a sphere are presented
here. The drag coefficient and surface pressures are calculated and compared with
available experimental and theoretical results. It is observed that these values simulated over coarser grids using the present scheme are more accurate when compared to
other conventional schemes. It has also been observed that the flow separation initially
occurred at Re=21. 相似文献
16.
Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit,Nesterov Accelerated Schemes
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Jea-Hyun Park Abner J. Salgado & Steven M. Wise 《Communications In Computational Physics》2023,33(2):367-398
We introduce a fast solver for the phase field crystal (PFC) and functionalized Cahn-Hilliard (FCH) equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov’s accelerated gradient descent
(PAGD) method. We discretize these problems with a Fourier collocation method
in space, and employ various second-order schemes in time. We observe a significant speedup with this solver when compared to the preconditioned gradient descent
(PGD) method. With the PAGD solver, fully implicit, second-order-in-time schemes
are not only feasible to solve the PFC and FCH equations, but also do so more efficiently than some semi-implicit schemes in some cases where accuracy issues are
taken into account. Benchmark computations of four different schemes for the PFC
and FCH equations are conducted and the results indicate that, for the FCH experiments, the fully implicit schemes (midpoint rule and BDF2 equipped with the PAGD
as a nonlinear time marching solver) perform better than their IMEX versions in terms
of computational cost needed to achieve a certain precision. For the PFC, the results
are not as conclusive as in the FCH experiments, which, we believe, is due to the fact
that the nonlinearity in the PFC is milder nature compared to the FCH equation. We
also discuss some practical matters in applying the PAGD. We introduce an averaged
Newton preconditioner and a sweeping-friction strategy as heuristic ways to choose good
preconditioner parameters. The sweeping-friction strategy exhibits almost as good
a performance as the case of the best manually tuned parameters. 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.
Yifei Wan & Yinhua Xia 《Communications In Computational Physics》2023,33(5):1270-1331
For steady Euler equations in complex boundary domains, high-order shockcapturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian
grids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-order
finite difference hybrid WENO scheme to simulate steady Euler equations, and the
same fifth-order WENO extrapolation methods are developed to handle the curved
boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform
the tangential derivatives along the curved solid wall boundary. This hybrid WENO
scheme is robust for steady-state convergence and maintains high-order accuracy in
the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows
that this hybrid WENO scheme has low dispersion and dissipation errors. Numerical
examples are presented to validate the high-order accuracy and robust performance of
the hybrid scheme for steady Euler equations in curved domains with Cartesian grids. 相似文献
19.
Shuang Tan Wenjun Sun Kun Xu Junxia Wei & Guoxi Ni 《Communications In Computational Physics》2020,28(3):1189-1218
In this paper, a time implicit unified gas kinetic scheme (IUGKS) for 3D
multi-group neutron transport equation with delayed neutron is developed. The
explicit scheme, implicit 1st-order backward Euler scheme, and 2nd-order Crank-Nicholson scheme, become the subsets of the current IUGKS. In neutron transport,
the microscopic angular flux and the macroscopic scalar flux are fully coupled in an
implicit way with the combination of dual-time step technique for the convergence acceleration of unsteady evolution. In IUGKS, the computational time step is no longer
limited by the Courant-Friedrichs-Lewy (CFL) condition, which improves the computational efficiency in both steady and unsteady simulations with a large time step.
Mathematically, the current scheme has the asymptotic preserving (AP) property in
recovering automatically the diffusion solution in the continuum regime. Since the
explicit scanning along neutron traveling direction within the computational domain
is not needed in IUGKS, the scheme can be easily extended to multi-dimensional and
parallel computations. The numerical tests demonstrate that the IUGKS has high computational efficiency, high accuracy, and strong robustness when compared with other
schemes, such as the explicit UGKS, the commonly used finite difference, and finite
volume methods. This study shows that the IUGKS can be used faithfully to study
neutron transport in practical engineering applications. 相似文献
20.
A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes
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In [SIAM J. Sci. Comput., 35(2)(2013), A1049–A1072], a class of multi-domain
hybrid DG and WENO methods for conservation laws was introduced. Recent applications of this method showed that numerical instability may encounter if the DG flux
with Lagrangian interpolation is applied as the interface flux during the moment of
conservative coupling. In this continuation paper, we present a more robust approach
in the construction of DG flux at the coupling interface by using WENO procedures of
reconstruction. Based on this approach, such numerical instability is overcome very
well. In addition, the procedure of coupling a DG method with a WENO-FD scheme
on hybrid meshes is disclosed in detail. Typical testing cases are employed to demonstrate the accuracy of this approach and the stability under the flexibility of using either
WENO-FD flux or DG flux at the moment of requiring conservative coupling. 相似文献