共查询到20条相似文献，搜索用时 15 毫秒
1.
Fu‐Zheng Gao Yi‐Rang Yuan 《Numerical Methods for Partial Differential Equations》2009,25(5):1067-1085
2.
Paul Deuring Marcus Mildner 《Numerical Methods for Partial Differential Equations》2012,28(2):402-424
We consider a time‐dependent and a stationary convection‐diffusion equation. These equations are approximated by a combined finite element – finite volume method: the diffusion term is discretized by Crouzeix‐Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the nonstationary case, we use an implicit Euler approach for time discretization. This scheme is shown to be L2‐stable uniformly with respect to the diffusion coefficient. In addition, it turns out that stability is unconditional in the time‐dependent case. These results hold if the underlying grid satisfies a condition that is fulfilled, for example, by some structured meshes. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 402–424, 2012 相似文献
3.
Samir Karaa 《Numerical Methods for Partial Differential Equations》2006,22(4):983-993
We derive a high‐order compact alternating direction implicit (ADI) method for solving three‐dimentional unsteady convection‐diffusion problems. The method is fourth‐order in space and second‐order in time. It permits multiple uses of the one‐dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second‐order Douglas‐Gunn ADI method and the spatial fourth‐order compact scheme by Karaa. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
4.
Chunjia Bi 《高等学校计算数学学报(英文版)》2006,15(1):82-96
In this paper,we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems. It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H~1-and L~2-norms. 相似文献
5.
对流扩散方程的一种显式有限体积——有限元方法 总被引：4，自引：0，他引：4
窦红 《应用数学与计算数学学报》2001,15(2):45-52
本文给出非线性对流扩散问题的一种有限体积的有限元方法相结合的显式离散方法,证明了数值解的稳定性,并给出了一个实际算例。 相似文献
6.
Paul Deuring 《Numerical Methods for Partial Differential Equations》2016,32(6):1591-1621
We consider a time‐dependent and a steady linear convection‐diffusion‐reaction equation whose coefficients are nonconstant. Boundary conditions are mixed (Dirichlet and Robin–Neumann) and nonhomogeneous. Both the unsteady and the steady problem are approximately solved by a combined finite element–finite volume method: the diffusion term is discretized by Crouzeix–Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. The ‐ and the ‐error in the unsteady case and the H1‐error in the steady one are estimated against the data, in such a way that no parameter enters exponentially into the constants involved. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1591–1621, 2016 相似文献
7.
Hong Wang Mohamed Al‐Lawatia 《Numerical Methods for Partial Differential Equations》2006,22(3):577-599
Characteristic methods generally generate accurate numerical solutions and greatly reduce grid orientation effects for transient advection‐diffusion equations. Nevertheless, they raise additional numerical difficulties. For instance, the accuracy of the numerical solutions and the property of local mass balance of these methods depend heavily on the accuracy of characteristics tracking and the evaluation of integrals of piecewise polynomials on some deformed elements generally with curved boundaries, which turns out to be numerically difficult to handle. In this article we adopt an alternative approach to develop an Eulerian‐Lagrangian control‐volume method (ELCVM) for transient advection‐diffusion equations. The ELCVM is locally conservative and maintains the accuracy of characteristic methods even if a very simple tracking is used, while retaining the advantages of characteristic methods in general. Numerical experiments show that the ELCVM is favorably comparable with well‐regarded Eulerian‐Lagrangian methods, which were previously shown to be very competitive with many well‐perceived methods. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
8.
We develop an upwind finite volume (UFV) scheme for unsteady‐state advection‐diffusion partial differential equations (PDEs) in multiple space dimensions. We apply an alternating direction implicit (ADI) splitting technique to accelerate the solution process of the numerical scheme. We investigate and analyze the reason why the conventional ADI splitting does not satisfy maximum principle in the context of advection‐diffusion PDEs. Based on the analysis, we propose a new ADI splitting of the upwind finite volume scheme, the alternating‐direction implicit, upwind finite volume (ADFV) scheme. We prove that both UFV and ADFV schemes satisfy maximum principle and are unconditionally stable. We also derive their error estimates. Numerical results are presented to observe the performance of these schemes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 211–226, 2003 相似文献
9.
In this paper, we consider a high order finite volume approximation of one‐dimensional nonlocal reactive flows of parabolic type. The method is obtained by discretizing in space by arbitrary order vertex‐centered finite volumes, followed by a modified Simpson quadrature scheme for the time stepping. Compared to the existed finite volume methods, this new finite volume scheme could achieve the desired accuracy with less data storage by employing higher‐order trial spaces. The finite volume approximations are proved to possess optimal order convergence rates in the H1‐norm and L2‐norm, which are also confirmed by numerical tests. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
T. Ismagilov 《Computational Mathematics and Mathematical Physics》2006,46(3):453-464
An integral conservation law is derived for smooth volume in Lagrangian coordinates (a comoving frame). A method for approximation
of the integral smooth volume conservation law is discussed. An extension technique is suggested for development of smooth
volume schemes. For hyperbolic systems, smooth volume upwind and Godunov schemes with monotonic reconstruction are derived.
The schemes are applied to equations of gas dynamics and tested for three gas-dynamics shock tube problems. The solutions
are monotonic and precise.
This article was submitted by the author in English. 相似文献
11.
王同科 《高等学校计算数学学报(英文版)》2002,11(2):213-225
1 ＩｎｔｒｏｄｕｃｔｉｏｎＦｉｎｉｔｅｖｏｌｕｍｅｅｌｅｍｅｎｔｍｅｔｈｏｄｏｒＦＶＥＭｕｓｅｓａｖｏｌｕｍｅｉｎｔｅｇｒａｌｆｏｒｍｕｌａｔｉｏｎｏｆｔｈｅｄｉｆ ｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｉｔｈａｆｉｎｉｔｅｐａｒｔｉｔｉｏｎｉｎｇｓｅｔｏｆｖｏｌｕｍｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｅｑｕａｔｉｏｎ ,ｔｈｅｎｒｅ ｓｔｒｉｃｔｓｔｈｅａｄｍｉｓｓｉｂｌｅｆｕｎｃｔｉｏｎｓｔｏａｌｉｎｅａｒｆｉｎｉｔｅｅｌｅｍｅｎｔｓｐａｃｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｓｏｌｕｔｉｏｎ ([1 -4 ] ) .… 相似文献
12.
《Numerical Methods for Partial Differential Equations》2018,34(2):602-625
Motivated by the idea that staggered‐grid methods give a greater stability and give energy conservation, this article presents a new family of high‐order implicit staggered‐grid finite difference methods with any order of accuracy to approximate partial differential equations involving second‐order derivatives. In particular, we numerically analyze our new methods for the solution of the one‐dimensional acoustic wave equation. The implicit formulation is based on the plane wave theory and the Taylor series expansion and only involves the solution of tridiagonal matrix equations resulting in an attractive method with higher order of accuracy but nearly the same computation cost as those of explicit formulation. The order of accuracy of the proposal staggered formulas are similar to the methods with conventional grids for a ‐point operator: the explicit formula is th‐order and the implicit formula is th‐order; however, the results demonstrate that new staggered methods are superior in terms of stability properties to the classical methods in the context of solving wave equations. 相似文献
13.
Dongyang Shi Hongbo Guan Wei Gong 《Mathematical Methods in the Applied Sciences》2014,37(8):1130-1136
A low order characteristic‐nonconforming finite element method is proposed for solving a two‐dimensional convection‐dominated transport problem. On the basis of the distinguish property of element, that is, the consistency error can be estimated as order O(h2), one order higher than that of its interpolation error, the superclose result in broken energy norm is derived for the fully discrete scheme. In the process, we use the interpolation operator instead of the so‐called elliptic projection, which is an indispensable tool in the traditional finite element analysis. Furthermore, the global superconvergence is obtained by using the interpolated postprocessing technique. Lastly, some numerical experiments are provided to verify our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
陈思思;李许龙;张超男;秦娟娟;赵秉新 《应用数学和力学》2024,45(12):1473-1482
采用高精度、高分辨率的数值方法,对三种方向的外磁场下长腔内不同液态金属双扩散对流的动力学特性进行直接数值模拟研究,揭示了流体物性参数Prandtl数(Pr)、磁场方向以及磁场强度对流动和传热传质的影响规律.结果表明：在所考察的Prandtl数范围内,随着Pr的增大,弱磁场时,流动从非定常的周期流动过渡为定常对流,其中Prandtl数为0.03时该对流系统存在非定常解,流动是周期性的,传热传质效率先快速增长,之后增速变缓;中等强度磁场时,流动始终是定常的,传热传质效率随Prandtl数增大的增速进一步减缓;强磁场时,流动总是定常的,传热传质效率几乎不随Prandtl数的改变而改变.在同一磁场强度下,相比于45°倾斜磁场和水平磁场,垂直磁场对传热传质效率产生的抑制作用较小. 相似文献
15.
Chuanjun Chen Wei Liu Chunjia Bi 《Numerical Methods for Partial Differential Equations》2013,29(5):1543-1562
A two‐grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time‐dependent advection‐dominated diffusion equations in two space dimensions. The solution of a nonlinear system on the fine‐grid space (with grid size h) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse‐grid space (with grid size H) and a linear system on the fine‐grid space. An optimal error estimate in H1 ‐norm is obtained for the two‐grid method. It shows that the two‐grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O(H2). Numerical example is presented to validate the usefulness and efficiency of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
16.
In this paper we present a finite volume method for solving Hamilton-Jacobi-Bellman(HJB) equations governing a class of optimal feedback control problems. This method is based on a finite volume discretization in state space coupled with an upwind finite difference technique, and on an implicit backward Euler finite differencing in time, which is absolutely stable. It is shown that the system matrix of the resulting discrete equation is an M-matrix. To show the effectiveness of this approach, numerical experiments on test problems with up to three states and two control variables were performed. The numerical results show that the method yields accurate approximate solutions to both the control and the state variables. 相似文献
17.
Yirang Yuan 《Numerical Methods for Partial Differential Equations》2006,22(3):661-679
In modern numerical simulation of prospecting and exploiting oil‐gas resources and in environmental science, it is necessary to consider numerical method of nonlinear convection‐dominated diffusion problems. This thesis, starting from actual conditions such as the three‐dimensional characteristics of large‐scale science‐engineering computation, puts forward a kind of characteristic finite element alternating direction method with moving meshes. Some techniques, such as calculus of variations, operator‐splitting, generalized L2 projection, energy method, negative norm estimate, the theory of prior estimates and techniques, are adopted. Optimal order estimates in L2 norm are derived to determine the errors in the approximate solution. Thus the important theoretical problem has been solved. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
18.
Mofdi El‐Amrani Mohammed Seaïd 《Numerical Methods for Partial Differential Equations》2008,24(3):776-798
We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier‐Stokes equations including density variation through the Boussinesq approximation. The solution procedure consists of combining an essentially non‐oscillatory modified method of characteristics for time discretization with finite element method for space discretization. These numerical techniques associate the geometrical flexibility of the finite elements with the ability offered by modified method of characteristics to solve convection‐dominated flows using time steps larger than its Eulerian counterparts. Numerical results are shown for natural convection in a squared cavity and heat transport in the strait of Gibraltar. Performance and accuracy of the method are compared to other published data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
19.
Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an appropriate, critical quadrature rule; this allows the elimination of the flux and Lagrange multiplier parameters so as to obtain equations in the scalar variable, which will define the finite volume method. Following this derivation with different mixed finite element spaces leads to a variety of finite volume schemes. In particular, we restrict ourselves to finite volume methods posed over rectangular partitions and begin by studying an efficient second-order finite volume method based on the Brezzi–Douglas–Fortin–Marini space of index two. Then, we present a general global analysis of the difference between the solution of the underlying mixed finite element method and its related finite volume method. Then, we derive finite volume methods of all orders from the Raviart–Thomas two-dimensional rectangular elements; we also find finite volume methods to associate with BDFM
2 three-dimensional rectangles. In each case, we obtain optimal error estimates for both the scalar variable and the recovered flux. 相似文献
20.
A simple weighted essentially non-oscillatory (SWENO) scheme for solving the convection-diffusion equation is proposed in this paper, where a seventh-order SWENO method and the third-order strong stability preserving (SSP) Runge-Kutta method are adopted for discretizing the space and time, respectively. Thenthe hyperbolic and diffusive part can achieve the seventh- and sixth-order accuracy,respectively. The proposed method has the following advantages. Firstly, negativelinear weights are avoided. Secondly, one reconstruction with one stencil is requiredfor the computation of convective and diffusive fluxes. Finally, the new methoddoes not require the transformation while the diffusion coefficients are degenerate. Numerical examples demonstrate that the new method can achieve sixth-orderaccuracy in the smooth region and guarantee non-oscillatory properties for the discontinuous problems for one- and two-dimensional cases. 相似文献