共查询到20条相似文献,搜索用时 31 毫秒
1.
A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
2.
Explicit time stepping schemes for the immersed boundary method require
very small time steps in order to maintain stability. Solving the equations that arise
from an implicit discretization is difficult. Recently, several different approaches have
been proposed, but a complete understanding of this problem is still emerging. A
multigrid method is developed and explored for solving the equations in an implicit-time discretization of a model of the immersed boundary equations. The model problem consists of a scalar Poisson equation with conformation-dependent singular forces
on an immersed boundary. This model does not include the inertial terms or the incompressibility constraint. The method is more efficient than an explicit method, but
the efficiency gain is limited. The multigrid method alone may not be an effective
solver, but when used as a preconditioner for Krylov methods, the speed-up over the
explicit-time method is substantial. For example, depending on the constitutive law
for the boundary force, with a time step 100 times larger than the explicit method,
the implicit method is about 15-100 times more efficient than the explicit method. A
very attractive feature of this method is that the efficiency of the multigrid preconditioned Krylov solver is shown to be independent of the number of immersed boundary
points. 相似文献
3.
A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Xin Lv Qingping Zou D. E. Reeve & Yong Zhao 《Communications In Computational Physics》2012,11(1):215-248
We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems. 相似文献
4.
Laurette S. Tuckerman 《Communications In Computational Physics》2015,18(5):1336-1351
Many physical processes are described by elliptic or parabolic partial differential
equations. For linear stability problems associated with such equations, the
inverse Laplacian provides a very effective preconditioner. In addition, it is also readily
available in most scientific calculations in the form of a Poisson solver or an implicit
diffusive time step. We incorporate Laplacian preconditioning into the inverse Arnoldi
method, using BiCGSTAB to solve the large linear systems. Two successful implementations
are described: spherical Couette flow described by the Navier-Stokes equations
and Bose-Einstein condensation described by the nonlinear Schrödinger equation. 相似文献
5.
An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
6.
A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We introduce and study a parallel domain decomposition algorithm for
the simulation of blood flow in compliant arteries using a fully-coupled system of
nonlinear partial differential equations consisting of a linear elasticity equation and
the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving
meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition
plays an interesting role in the accuracy of the blood flow simulation and we provide a
numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition
method for solving the fully coupled nonlinear system on a supercomputer with a few
hundred processors. 相似文献
7.
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
8.
An Efficient Parallel/Unstructured-Multigrid Implicit Method for Simulating 3D Fluid-Structure Interaction
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
9.
A Simple Solver for the Two-Fluid Plasma Model Based on PseudoSpectral Time-Domain Algorithm
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Benoit Morel Remo Giust Kazem Ardaneh & Francois Courvoisier 《Communications In Computational Physics》2021,29(3):955-978
We present a solver of 3D two-fluid plasma model for the simulation of
short-pulse laser interactions with plasma. This solver resolves the equations of the
two-fluid plasma model with ideal gas closure. We also include the Bhatnagar-Gross-Krook collision model. Our solver is based on PseudoSpectral Time-Domain (PSTD)
method to solve Maxwell's curl equations. We use a Strang splitting to integrate Euler
equations with source term: while Euler equations are solved with a composite scheme
mixing Lax-Friedrichs and Lax-Wendroff schemes, the source term is integrated with
a fourth-order Runge-Kutta scheme. This two-fluid plasma model solver is simple to
implement because it only relies on finite difference schemes and Fast Fourier Transforms. It does not require spatially staggered grids. The solver was tested against
several well-known problems of plasma physics. Numerical simulations gave results
in excellent agreement with analytical solutions or with previous results from the literature. 相似文献
10.
Xiaoqiang Yue Shi Shu Xiaowen Xu & Zhiyang Zhou 《Communications In Computational Physics》2015,18(5):1313-1335
The paper aims to develop an effective preconditioner and conduct the convergence
analysis of the corresponding preconditioned GMRES for the solution of discrete
problems originating from multi-group radiation diffusion equations. We firstly
investigate the performances of the most widely used preconditioners (ILU(k) and
AMG) and their combinations ($B_{co}$ and$\widetilde{B}_{co}$), and provide drawbacks on their feasibilities.
Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing
the features suitable for AMG using more detailed measurements on multiscale
nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present
an adaptive combined preconditioner $B^α_{co}$ involving an improved ILU(0) along with
its convergence constraints. Numerical results demonstrate that $B^α_{co}$-GMRES holds the
best robustness and efficiency. At last, we analyze the convergence of GMRES with
combined preconditioning which not only provides a persuasive support for our proposed
algorithms, but also updates the existing estimation theory on condition numbers
of combined preconditioned systems. 相似文献
11.
In this paper, preconditioned iterative methods for solving two-dimensional
space-fractional diffusion equations are considered. The fractional diffusion equation
is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson
weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian,
H. Zhou and W. Deng, A class of second order difference approximation for solving space
fractional diffusion equations, Math. Comp., 84 (2015) 1703-1727]. For the discretized
linear systems, we first propose preconditioned iterative methods to solve them. Then
we apply the D'Yakonov ADI scheme to split the linear systems and solve the obtained
splitting systems by iterative methods. Two preconditioned iterative methods, the preconditioned
generalized minimal residual (preconditioned GMRES) method and the
preconditioned conjugate gradient normal residual (preconditioned CGNR) method,
are proposed to solve relevant linear systems. By fully exploiting the structure of the
coefficient matrix, we design two special kinds of preconditioners, which are easily
constructed and are able to accelerate convergence of iterative solvers. Numerical
results show the efficiency of our preconditioners. 相似文献
12.
Adaptive Fully Implicit Simulator with Multilevel Schwarz Methods for Gas Reservoir Flows in Fractured Porous Media
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
13.
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active-set strategy, called PRESAS , for the efficient solution of such block-sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank-one factorization updates of the preconditioner result in a per-iteration computational complexity of , where m denotes the number of state and control variables and N the number of control intervals. Three different block-structured preconditioning techniques are presented and their numerical properties are studied further. In addition, an augmented Lagrangian based implementation is proposed to avoid a costly initialization procedure to find a primal feasible starting point. Based on a standalone C code implementation, we illustrate the computational performance of PRESAS against current state of the art QP solvers for multiple linear and nonlinear MPC case studies. We also show that the solver is real-time feasible on a dSPACE MicroAutoBox-II rapid prototyping unit for vehicle control applications, and numerical reliability is illustrated based on experimental results from a testbench of small-scale autonomous vehicles. 相似文献
14.
In this paper, we will develop a fast iterative solver for the system of linear
equations arising from the local discontinuous Galerkin (LDG) spatial discretization
and additive Runge-Kutta (ARK) time marching method for the KdV type equations.
Being implicit in time, the severe time step ($∆t$=$\mathcal{O}(∆x^k)$, with the $k$-th order of the
partial differential equations (PDEs)) restriction for explicit methods will be removed.
The equations at the implicit time level are linear and we demonstrate an efficient,
practical multigrid (MG) method for solving the equations. In particular, we numerically
show the optimal or sub-optimal complexity of the MG solver and a two-level
local mode analysis is used to analyze the convergence behavior of the MG method.
Numerical results for one-dimensional, two-dimensional and three-dimensional cases
are given to illustrate the efficiency and capability of the LDG method coupled with
the multigrid method for solving the KdV type equations. 相似文献
15.
A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Tiao Lu Gang Du Xiaoyan Liu & Pingwen Zhang 《Communications In Computational Physics》2011,10(2):305-338
We propose a deterministic solver for the time-dependent multi-subband
Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in
double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared
out source/drain contacts. A realistic model with six-valleys of the conduction band
of silicon and both intra-valley and inter-valley phonon-electron scattering is solved.
We propose a second order finite volume method based on the positive and flux conservative
(PFC) method to discretize the Boltzmann transport equations (BTEs). The
transport part of the BTEs is split into two problems. One is a 1D transport problem in
the position space, and the other is a 2D transport problem in the wavevector space. In
order to reduce the splitting error, the 2D transport problem in the wavevector space
is solved directly by using the PFC method instead of splitting into two 1D problems.
The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic
is investigated. Comparison of the numerical results with ballistic solutions
show that the scattering influence is not ignorable even when the size of a nanoscale
semiconductor device goes to the scale of the electron mean free path. 相似文献
16.
A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Numerically solving 3D seismic wave equations is a key requirement for
forward modeling and inversion. Here, we propose a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for 3D acoustic and elastic wave-field modeling. For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, and
then we use a discontinuous Galerkin (DG) solver based on numerical-flux formulations for spatial discretization. The time discretization is based on an implicit diagonal Runge-Kutta (RK) method and an explicit iterative technique, which avoids
solving a large-scale system of linear equations. In the iterative process, we introduce
a weighting factor. We investigate the numerical stability criteria of the 3D method in
detail for linear and quadratic spatial basis functions. We also present a 3D analysis of
numerical dispersion for the full discrete approximation of acoustic equation, which
demonstrates that the WRKDG method can efficiently suppress numerical dispersion
on coarse grids. Numerical results for several different 3D models including homogeneous and heterogeneous media with isotropic and anisotropic cases show that the 3D
WRKDG method can effectively suppress numerical dispersion and provide accurate
wave-field information on coarse mesh. 相似文献
17.
This paper is concerned with a new version of the Osher-Solomon Riemann
solver and is based on a numerical integration of the path-dependent dissipation matrix.
The resulting scheme is much simpler than the original one and is applicable to
general hyperbolic conservation laws, while retaining the attractive features of the original
solver: the method is entropy-satisfying, differentiable and complete in the sense
that it attributes a different numerical viscosity to each characteristic field, in particular
to the intermediate ones, since the full eigenstructure of the underlying hyperbolic system
is used. To illustrate the potential of the proposed scheme we show applications
to the following hyperbolic conservation laws: Euler equations of compressible gasdynamics
with ideal gas and real gas equation of state, classical and relativistic MHD
equations as well as the equations of nonlinear elasticity. To the knowledge of the authors,
apart from the Euler equations with ideal gas, an Osher-type scheme has never
been devised before for any of these complicated PDE systems. Since our new general
Riemann solver can be directly used as a building block of high order finite volume
and discontinuous Galerkin schemes we also show the extension to higher order of
accuracy and multiple space dimensions in the new framework of PNPM schemes on
unstructured meshes recently proposed in [9]. 相似文献
18.
An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Laiping Zhang Ming Li Wei Liu & Xin He 《Communications In Computational Physics》2015,17(1):287-316
A Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicit
method was developed to solve two-dimensional Euler and Navier-Stokes equations
by the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employed
to solve the nonlinear system, while the linear system was solved with LU-SGS iteration.
The effect of several parameters in the implicit scheme, such as the CFL number,
the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was investigated
to evaluate the performance of convergence history. Several typical test
cases were simulated, and compared with the traditional explicit Runge-Kutta (RK)
scheme. Firstly the Couette flow was tested to validate the order of accuracy of the
present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channel
was simulated and the effect of parameters was alsoinvestigated. Finally, the implicit
algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder
and the viscous flow in a square cavity. The numerical results demonstrated that
the present implicit scheme can accelerate the convergence history efficiently. Choosing
proper parameters would improve the efficiency of the implicit scheme. Moreover,
in the same framework, the DG/FV hybrid schemes are more efficient than the same
order DG schemes. 相似文献
19.
Philipp Neumann Hans-Joachim Bungartz Miriam Mehl Tobias Neckel & Tobias Weinzierl 《Communications In Computational Physics》2012,12(1):65-84
We couple different flow models, i.e. a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton, using the framework Peano as a
common base. The new coupling strategy between the meso- and macroscopic solver
is presented and validated in a 2D channel flow scenario. The results are in good
agreement with theory and results obtained in similar works by Latt et al. In addition,
the test scenarios show an improved stability of the coupled method compared to pure
Lattice Boltzmann simulations. 相似文献
20.
A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient
下载免费PDF全文
![点击此处可从《Communications In Computational Physics》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We propose a direct solver for the three-dimensional Poisson equation with
a variable coefficient, and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient matrix. Introducing
some appropriate finite difference operators, we derive a second-order scheme for the
solver, and then two suitable high-order compact schemes are also discussed. For
a cube containing N nodes, the solver requires O(N3/2log2N) arithmetic operations
and O(NlogN) memory to store the necessary information. Its efficiency is illustrated
with examples, and the numerical results are analysed. 相似文献