共查询到20条相似文献，搜索用时 15 毫秒
1.
S. Faure 《Numerical Methods for Partial Differential Equations》2005,21(2):242-271
The aim of this article is to describe a colocated finite volume approximation of the incompressible Navier‐Stokes equation and study its stability. One of the advantages of colocated finite volume space discretizations over staggered space discretizations is that all the variables share the same location; hence, the possibility to more easily use complex geometries and hierarchical decompositions of the unknowns. The time discretization used in the scheme studied here is a projection method. First, we give the full discretization of the incompressible Navier‐Stokes equations, then, we state the stability result and prove it following the methods of Marion and Temam. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
2.
Christophe Berthon Françoise Foucher Tomás Morales 《Numerical Methods for Partial Differential Equations》2015,31(5):1396-1423
We consider the numerical approximation of the weak solutions of the two‐layer shallow‐water equations. The model under consideration is made of two usual one‐layer shallow‐water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one‐layer shallow‐water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow‐water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non‐negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015 相似文献
3.
This article investigates the finite‐time stability, stabilization, and boundedness problems for switched nonlinear systems with time‐delay. Unlike the existing average dwell‐time technique based on time‐dependent switching strategy, largest region function strategy, that is, state‐dependent switching control strategy is adopted to design the switching signal, which does not require the switching instants to be given in advance. Some sufficient conditions which guarantee finite‐time stable, stabilization, and boundedness of switched nonlinear systems with time‐delay are presented in terms of linear matrix inequalities. Detail proofs are given using multiple Lyapunov‐like functions. A numerical example is given to illustrate the effectiveness of the proposed methods. © 2014 Wiley Periodicals, Inc. Complexity 21: 267–275, 2015 相似文献
4.
B.E. Flores J.P. Hennart E. del Valle 《Numerical Methods for Partial Differential Equations》2006,22(6):1348-1360
It is shown how mesh‐centered finite differences can be obtained from unconventional mixed‐hybrid nodal finite elements. The classical Raviart‐Thomas schemes of index k (RTk) are based on interpolation parameters that are cell and/or edge moments. For the unconventional form (URTk), they become point values at Gaussian points. In particular, the scheme URT1 is fully described. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 相似文献
5.
Linda El Alaoui Alexandre Ern 《Numerical Methods for Partial Differential Equations》2006,22(5):1106-1126
A nonconforming (Crouzeix–Raviart) finite element method with subgrid viscosity is analyzed to approximate advection‐diffusion‐reaction equations. The error estimates are quasi‐optimal in the sense that keeping the Péclet number fixed, the estimates are suboptimal of order in the mesh size for the L2‐norm and optimal for the advective derivative on quasi‐uniform meshes. The method is also reformulated as a finite volume box scheme providing a reconstruction formula for the diffusive flux with local conservation properties. Numerical results are presented to illustrate the error analysis. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
6.
Weizhong Dai Guang Li Raja Nassar Shengjun Su 《Numerical Methods for Partial Differential Equations》2005,21(6):1140-1154
7.
The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
8.
Cheng Wang Mingyan He Pengtao Sun 《Numerical Methods for Partial Differential Equations》2016,32(3):799-818
In this article, we develop a combined finite element‐weighted upwind finite volume method for convection‐dominated diffusion problems in two dimensions, which discretizes the diffusion term with the standard finite element scheme, and the convection and source terms with the weighted upwind finite volume scheme. The developed method leads to a totally new scheme for convection‐dominated problems, which overcomes numerical oscillation, avoids numerical dispersion, and has high‐order accuracy. Stability analyses of the scheme are given for the problems with constant coefficients. Numerical experiments are presented to illustrate the stability and optimal convergence of our proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 799–818, 2016 相似文献
9.
A. Serghini Mounim 《Numerical Methods for Partial Differential Equations》2008,24(2):368-382
A space‐time finite element method is introduced to solve the linear damped wave equation. The scheme is constructed in the framework of the mixed‐hybrid finite element methods, and where an original conforming approximation of H(div;Ω) is used, the latter permits us to obtain an upwind scheme in time. We establish the link between the nonstandard finite difference scheme recently introduced by Mickens and Jordan and the scheme proposed. In this regard, two approaches are considered and in particular we employ a formulation allowing the solution to be marched in time, i.e., one only needs to consider one time increment at a time. Numerical results are presented and compared with the analytical solution illustrating good performance of the present method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
10.
Hossein Mahmoodi Darian Reza Bozorgpour Maziar Shafaee 《Numerical Methods for Partial Differential Equations》2019,35(6):2375-2406
In the present paper, a hybrid filter is introduced for high accurate numerical simulation of shock‐containing flows. The fourth‐order compact finite difference scheme is used for the spatial discretization and the third‐order Runge–Kutta scheme is used for the time integration. After each time‐step, the hybrid filter is applied on the results. The filter is composed of a linear sixth‐order filter and the dissipative part of a fifth‐order weighted essentially nonoscillatory scheme (WENO5). The classic WENO5 scheme and the WENO5 scheme with adaptive order (WENO5‐AO) are used to form the hybrid filter. Using a shock‐detecting sensor, the hybrid filter reduces to the linear sixth‐order filter in smooth regions for damping high frequency waves and reduces to the WENO5 filter at shocks in order to eliminate unwanted oscillations produced by the nondissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the advection, Euler and Navier–Stokes equations. The results are compared with that of a hybrid second‐order filter and also that of the WENO5 and WENO5‐AO schemes. 相似文献
11.
This paper deals with the dynamics of a class of hybrid dynamical systems, which are subject to time‐dependent impulsive perturbations within a finite‐time interval and describe control strategies for integrated pest management. By using suitably defined Lyapunov functionals, sufficient conditions for the finite‐time contractive stability of the null solution are found by means of monotonicity arguments. Finally, a numerical simulation illustrates the theoretical analysis. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
Ritesh Kumar Dubey Prabhat Mishra 《Numerical Methods for Partial Differential Equations》2023,39(1):108-132
It is well known that on uniform mesh classical higher order schemes for evolutionary problems yield an oscillatory approximation of the solution containing discontinuity or boundary layers. In this article, an entirely new approach for constructing locally adaptive mesh is given to compute nonoscillatory solution by representative “second” order schemes. This is done using modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation. The proposed algorithm is applied on scalar problems to compute the solution with discontinuity or boundary layer. Presented numerical results show underlying second order schemes approximate discontinuities and boundary layers without spurious oscillations. 相似文献
13.
T. N. Phillips A. J. Williams 《Numerical Methods for Partial Differential Equations》2001,17(4):403-425
Semi‐Lagrangian finite volume schemes for the numerical approximation of linear advection equations are presented. These schemes are constructed so that the conservation properties are preserved by the numerical approximation. This is achieved using an interpolation procedure based on area‐weighting. Numerical results are presented illustrating some of the features of these schemes. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:403–425, 2001 相似文献
14.
We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH. 相似文献
15.
Tomás Morales de Luna Manuel J. Castro Díaz Carlos Parés 《Numerical Methods for Partial Differential Equations》2014,30(4):1315-1341
Approximate Riemann solvers (ARS) and polynomial viscosity matrix (PVM) methods constitute two general frameworks to derive numerical schemes for hyperbolic systems of Partial Differential Equations (PDE's). In this work, the relation between these two frameworks is analyzed: we show that every PVM method can be interpreted in terms of an approximate Riemann solver provided that it is based on a polynomial that interpolates the absolute value function at some points. Furthermore, the converse is true provided that the ARS satisfies a technical property to be specified. Besides its theoretical interest, this relation provides a useful tool to investigate the properties of some well‐known numerical methods that are particular cases of PVM methods, as the analysis of some properties is easier for ARS methods. We illustrate this usefulness by analyzing the positivity‐preservation property of some well‐known numerical methods for the shallow water system. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1315–1341, 2014 相似文献
16.
Christine Kaland Jens Struckmeier 《Mathematical Methods in the Applied Sciences》2008,31(16):1922-1945
The Savage–Hutter (SH) equations describe the motion of granular material under the influence of friction. Based on the kinetic formulation of the SH equations, we present a kinetic scheme in one dimension, which describes the deformation of the mass profile and allows it to start and to stop. Moreover the method is able to preserve the steady states of granular masses at rest. The method is tested on several numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory 相似文献
18.
Xianping Li Weizhang Huang 《Numerical Methods for Partial Differential Equations》2013,29(6):1963-1985
Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the θ ‐method in time for solving time‐dependent anisotropic diffusion problems. It is shown that the numerical solution satisfies a discrete maximum principle when all element angles of the mesh measured in the metric specified by the inverse of the diffusion matrix are nonobtuse, and the time step size is bounded below and above by bounds proportional essentially to the square of the maximal element diameter. The lower bound requirement can be removed when a lumped mass matrix is used. In two dimensions, the mesh and time step conditions can be replaced by weaker Delaunay‐type conditions. Numerical results are presented to verify the theoretical findings. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
19.
《Numerical Methods for Partial Differential Equations》2018,34(6):2180-2216
In this article, we develop several first order fully discrete Galerkin finite element schemes for the Oldroyd model and establish the corresponding stability results for these numerical schemes with smooth and nonsmooth initial data. The stable mixed finite element method is used to the spatial discretization, and the temporal treatments of the spatial discrete Oldroyd model include the first order implicit, semi‐implicit, implicit/explicit, and explicit schemes. The ‐stability results of the different numerical schemes are provided, where the first‐order implicit and semi‐implicit schemes are the ‐unconditional stable, the implicit/explicit scheme is the ‐almost unconditional stable, and the first order explicit scheme is the ‐conditional stable. Finally, some numerical investigations of the ‐stability results of the considered numerical schemes for the Oldroyd model are provided to verify the established theoretical findings. 相似文献
20.
Silvia Jerez 《Numerical Methods for Partial Differential Equations》2013,29(6):2133-2145
In this work, we present a monotone first‐order weighted (FORWE) method for scalar conservation laws using a variational formulation. We prove theoretical properties as consistency, monotonicity, and convergence of the proposed scheme for the one‐dimensional (1D) Cauchy problem. These convergence results are extended to multidimensional scalar conservation laws by a dimensional splitting technique. For the validation of the FORWE method, we consider some standard bench‐mark tests of bidimensional and 1D conservation law equations. Finally, we analyze the accuracy of the method with L1 and L∞ error estimates. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献