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Journal articles on the topic 'Problème de Convection-diffusion'

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Published: 7 July 2024

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1

Gaultier, Maurice, and Mikel Lezaun. "Un problème de convection-diffusion avec réaction chimique." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 2 (January 1997): 159–64. http://dx.doi.org/10.1016/s0764-4442(99)80336-x.

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2

Ben-Abdallah, Philippe, Hamou Sadat, and Vital Le Dez. "Résolution d'un problème inverse de convection–diffusion par une méthode de perturbation singulière." International Journal of Thermal Sciences 39, no. 7 (July 2000): 742–52. http://dx.doi.org/10.1016/s1290-0729(00)00279-9.

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3

Dalík, Josef. "A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems." Applications of Mathematics 36, no. 5 (1991): 329–54. http://dx.doi.org/10.21136/am.1991.104471.

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4

Martynova, T. S., G. V. Muratova, I. N. Shabas, and V. V. Bavin. "Многосеточные методы с косо-эрмитовыми сглаживателями для задач конвекции–диффузии с преобладающей конвекцией." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 1 (January 31, 2022): 46–59. http://dx.doi.org/10.26089/nummet.v23r104.

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Abstract:

The convection–diffusion equation with dominant convection is considered on a uniform grid of central difference scheme. The multigrid method is used for solving the strongly nonsymmetric systems of linear algebraic equations with positive definite coefficient matrices. Two-step skew-Hermitian iterative methods are utilized for the first time as a smoothing procedure. It is demonstrated that using the proper smoothers enables to improve the convergence of the multigrid method. The robustness of the smoothers with respect to variation of the Peclet number is shown by local Fourier analysis and numerical experiments. Уравнение конвекции–диффузии с преобладающей конвекцией рассматривается на равномерной сетке центрально-разностной схемы. Многосеточный метод используется длярешения сильно несимметричных систем линейных алгебраических уравнений с положительно определенными матрицами коэффициентов. Двухшаговые косоэрмитовы итерационные методы впервые используются в качестве сглаживающей процедуры. Демонстрируется, что надлежащий выбор сглаживателей позволяет улучшить сходимость многосеточного метода. Локальный фурье-анализ и численные эксперименты приводят к выводу об устойчивости сглаживателей по отношению к изменению числа Пекле.

5

Dalík, Josef, and Helena Růžičková. "An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection." Applications of Mathematics 40, no. 5 (1995): 367–80. http://dx.doi.org/10.21136/am.1995.134300.

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6

Dolejší, V., M. Feistauer, and C. Schwab. "On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow." Mathematica Bohemica 127, no. 2 (2002): 163–79. http://dx.doi.org/10.21136/mb.2002.134171.

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7

Goldstein, C. I. "Preconditioning convection dominated convection‐diffusion problems." International Journal of Numerical Methods for Heat & Fluid Flow 5, no. 2 (February 1995): 99–119. http://dx.doi.org/10.1108/eum0000000004059.

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8

Stynes, Martin. "Steady-state convection-diffusion problems." Acta Numerica 14 (April 19, 2005): 445–508. http://dx.doi.org/10.1017/s0962492904000261.

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In convection-diffusion problems, transport processes dominate while diffusion effects are confined to a relatively small part of the domain. This state of affairs means that one cannot rely on the formal ellipticity of the differential operator to ensure the convergence of standard numerical algorithms. Thus new ideas and approaches are required.The survey begins by examining the asymptotic nature of solutions to stationary convection-diffusion problems. This provides a suitable framework for the understanding of these solutions and the difficulties that numerical techniques will face. Various numerical methods expressly designed for convection-diffusion problems are then presented and extensively discussed. These include finite difference and finite element methods and the use of special meshes.

9

Kashyap, Pradeep. "Convection Diffusion Problems Solved by Fractional Variational Iteration Method." RESEARCH HUB International Multidisciplinary Research Journal 9, no. 3 (March 23, 2022): 01–07. http://dx.doi.org/10.53573/rhimrj.2022.v09i03.001.

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The paper considers the application of FVIM. The method is exploited explaining convection diffusion problems in different physical situations. These physical situations include energy, particles, etc., are transmitted inside the system owed to diffusion-convection.

10

Roos, Hans-Görg, and Martin Stynes. "Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers." Applications of Mathematics 41, no. 4 (1996): 269–80. http://dx.doi.org/10.21136/am.1996.134326.

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11

Shih, Yin-Tzer, and Howard C. Elman. "Modified streamline diffusion schemes for convection-diffusion problems." Computer Methods in Applied Mechanics and Engineering 174, no. 1-2 (May 1999): 137–51. http://dx.doi.org/10.1016/s0045-7825(98)00283-7.

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12

Chang, Jen-Yi, Ru-Yun Chen, and Chia-Cheng Tsai. "Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems." Mathematics 10, no. 2 (January 7, 2022): 188. http://dx.doi.org/10.3390/math10020188.

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This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

13

Axelsson, O., and W. Layton. "Defect correction methods for convection dominated convection-diffusion problems." ESAIM: Mathematical Modelling and Numerical Analysis 24, no. 4 (1990): 423–55. http://dx.doi.org/10.1051/m2an/1990240404231.

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14

Borne, Sabine Le. "ℋ-matrices for Convection-diffusion Problems with Constant Convection." Computing 70, no. 3 (June 2003): 261–74. http://dx.doi.org/10.1007/s00607-003-1474-4.

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15

Kim, Yon-Chol. "A Compact Higher-Order Scheme for Two-Dimensional Unsteady Convection–Diffusion Equations." International Journal of Computational Methods 17, no. 07 (August 15, 2019): 1950025. http://dx.doi.org/10.1142/s0219876219500257.

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In this paper, we study a compact higher-order scheme for the two-dimensional unsteady convection–diffusion problems using the nearly analytic discrete method (NADM), especially, focusing on the convection dominated-diffusion problems. The numerical scheme is constructed and the stability analysis is implemented. We find the order of accuracy of scheme is [Formula: see text], where [Formula: see text] is the size of time steps and [Formula: see text] the size of spacial steps, especially, making clear the relation between [Formula: see text] and [Formula: see text] is according to the different values of diffusion parameter [Formula: see text] through von Neumann stability analysis. The obtained numerical results for several benchmark problems show that our method makes progress in the numerical study of NADM for convection–diffusion equation and is to be effective and helpful particularly in computations for the convection dominated-diffusion equations and, furthermore, valuable in the numerical treatment of many real-world problems such as MHD natural convection flow.

16

Tawil, Magdy A. El. "Stochastic Diffusion-Convection Boundary Value Problems." Chaos, Solitons & Fractals 9, no. 12 (December 1998): 1945–54. http://dx.doi.org/10.1016/s0960-0779(98)00007-1.

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17

Zhang, Yang. "AD–FDSD for convection–diffusion problems." Applied Mathematics and Computation 206, no. 1 (December 2008): 257–71. http://dx.doi.org/10.1016/j.amc.2008.02.025.

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18

Shi, Feng, Guoping Liang, Yubo Zhao, and Jun Zou. "New Splitting Methods for Convection-Dominated Diffusion Problems and Navier-Stokes Equations." Communications in Computational Physics 16, no. 5 (November 2014): 1239–62. http://dx.doi.org/10.4208/cicp.031013.030614a.

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AbstractWe present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is solved explicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme; while the diffusion subproblem is always self-adjoint and coercive so that they can be solved efficiently using many existing optimal preconditioned iterative solvers. The scheme can be extended for solving the Navier-Stokes equations, where the nonlinearity is resolved by a linear explicit multistep scheme at the convection step, while only a generalized Stokes problem is needed to solve at the diffusion step and the major stiffness matrix stays invariant in the time marching process. Numerical simulations are presented to demonstrate the stability, convergence and performance of the single-step and multistep variants of the new scheme.

19

Geng, Fazhan, Suping Qian, and Shuai Li. "Numerical solutions of singularly perturbed convection-diffusion problems." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 6 (July 29, 2014): 1268–74. http://dx.doi.org/10.1108/hff-01-2013-0033.

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Purpose – The purpose of this paper is to find an effective numerical method for solving singularly perturbed convection-diffusion problems. Design/methodology/approach – The present method is based on the asymptotic expansion method and the variational iteration method (VIM). First a zeroth order asymptotic expansion for the solution of the given singularly perturbed convection-diffusion problem is constructed. Then the reduced terminal value problem is solved by using the VIM. Findings – Two numerical examples are introduced to show the validity of the present method. Obtained numerical results show that the present method can provide very accurate analytical approximate solutions not only in the boundary layer, but also away from the layer. Originality/value – The combination of the asymptotic expansion method and the VIM is applied to singularly perturbed convection-diffusion problems.

20

Hansbo, Peter. "The characteristic streamline diffusion method for convection-diffusion problems." Computer Methods in Applied Mechanics and Engineering 96, no. 2 (April 1992): 239–53. http://dx.doi.org/10.1016/0045-7825(92)90134-6.

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21

Phongthanapanich, Sutthisak, and Pramote Dechaumphai. "A CHARACTERISTIC-BASED FINITE VOLUME ELEMENT METHOD FOR CONVECTION-DIFFUSION-REACTION EQUATION." Transactions of the Canadian Society for Mechanical Engineering 32, no. 3-4 (September 2008): 549–60. http://dx.doi.org/10.1139/tcsme-2008-0037.

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A two-dimensional convection-diffusion-reaction equation is discretized by the finite volume element method on triangular meshes. Time-dependent convection-diffusion-reaction equation is developed along the characteristic path using the characteristic-based scheme, while the finite volume method is employed for deriving the discretized equations. The concept of the finite element technique is applied to estimate the gradient quantities at the cell faces of the finite volume. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. The robustness and the accuracy of the method have been evaluated by using available analytical and numerical solutions of the pure-convection, convection-diffusion and convection-diffusion-reaction problems.

22

Cawood, M. E., V. J. Ervin, W. J. Layton, and J. M. Maubach. "Adaptive defect correction methods for convection dominated, convection diffusion problems." Journal of Computational and Applied Mathematics 116, no. 1 (April 2000): 1–21. http://dx.doi.org/10.1016/s0377-0427(99)00278-2.

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23

Muratova, Galina V., and Evgeniya M. Andreeva. "Multigrid method for solving convection-diffusion problems with dominant convection." Journal of Computational and Applied Mathematics 226, no. 1 (April 2009): 77–83. http://dx.doi.org/10.1016/j.cam.2008.05.055.

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24

Afanas'eva, Nadyezhda M., Alexander G. Churbanov, and Petr N. Vabishchevich. "Unconditionally Monotone Schemes for Unsteady Convection-Diffusion Problems." Computational Methods in Applied Mathematics 13, no. 2 (April 1, 2013): 185–205. http://dx.doi.org/10.1515/cmam-2013-0002.

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Abstract. This paper deals with constructing monotone schemes of the second-order accuracy in space for transient convection-diffusion problems. They are based on a reformulation of the convective and diffusive transport terms using the convective terms in the divergent and nondivergent forms. The stability of the difference schemes is established in the uniform and L1 norm. For 2D problems, unconditionally monotone schemes of splitting with respect to spatial variables are developed. Unconditionally stable schemes for problems of convection-diffusion-reaction are proposed, too.

25

Afanas’eva, N. M., P. N. Vabishchevich, and M. V. Vasil’eva. "Unconditionally stable schemes for convection-diffusion problems." Russian Mathematics 57, no. 3 (February 27, 2013): 1–11. http://dx.doi.org/10.3103/s1066369x13030018.

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26

Stynes, M. "Finite volume methods for convection-diffusion problems." Irish Mathematical Society Bulletin 0034 (1995): 49. http://dx.doi.org/10.33232/bims.0034.49.

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27

Dautov, R. Z., and E. M. Fedotov. "HDG schemes for stationary convection-diffusion problems." IOP Conference Series: Materials Science and Engineering 158 (November 2016): 012028. http://dx.doi.org/10.1088/1757-899x/158/1/012028.

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28

CHEN, Zhiming. "Adaptive computation for convection dominated diffusion problems." Science in China Series A 47, no. 7 (2004): 22. http://dx.doi.org/10.1360/04za0002.

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29

Bertoluzza, S., C. Canuto, and A. Tabacco. "Negative norm stabilization of convection-diffusion problems." Applied Mathematics Letters 13, no. 4 (May 2000): 121–27. http://dx.doi.org/10.1016/s0893-9659(99)00221-9.

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30

Dolejší, Vít. "hp-DGFEM for nonlinear convection-diffusion problems." Mathematics and Computers in Simulation 87 (January 2013): 87–118. http://dx.doi.org/10.1016/j.matcom.2013.03.001.

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31

Vabishchevich, P. N., and P. E. Zakharov. "Alternating triangular schemes for convection–diffusion problems." Computational Mathematics and Mathematical Physics 56, no. 4 (April 2016): 576–92. http://dx.doi.org/10.1134/s096554251604014x.

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32

Pyatkov, S. G., and E. I. Safonov. "Some Inverse Problems for Convection-Diffusion Equations." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 7, no. 4 (2014): 36–50. http://dx.doi.org/10.14529/mmp140403.

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33

Mužík, Juraj. "Boundary Knot Method for Convection-diffusion Problems." Procedia Engineering 111 (2015): 582–88. http://dx.doi.org/10.1016/j.proeng.2015.07.048.

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34

Linß, Torsten. "Layer-adapted meshes for convection–diffusion problems." Computer Methods in Applied Mechanics and Engineering 192, no. 9-10 (February 2003): 1061–105. http://dx.doi.org/10.1016/s0045-7825(02)00630-8.

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35

Lazarov, R. D., Ilya D. Mishev, and P. S. Vassilevski. "Finite Volume Methods for Convection-Diffusion Problems." SIAM Journal on Numerical Analysis 33, no. 1 (February 1996): 31–55. http://dx.doi.org/10.1137/0733003.

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36

Blanchard, D., and A. Porretta. "Stefan problems with nonlinear diffusion and convection." Journal of Differential Equations 210, no. 2 (March 2005): 383–428. http://dx.doi.org/10.1016/j.jde.2004.06.012.

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37

Linß, Torsten. "Solution Decompositions for Linear Convection-Diffusion Problems." Zeitschrift für Analysis und ihre Anwendungen 21, no. 1 (2002): 209–14. http://dx.doi.org/10.4171/zaa/1073.

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38

Ortiz, M. "A variational formulation for convection-diffusion problems." International Journal of Engineering Science 23, no. 7 (January 1985): 717–31. http://dx.doi.org/10.1016/0020-7225(85)90004-7.

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39

Stynes, Martin. "Finite volume methods for convection-diffusion problems." Journal of Computational and Applied Mathematics 63, no. 1-3 (November 1995): 83–90. http://dx.doi.org/10.1016/0377-0427(95)00056-9.

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40

Murphy, J. D., and P. M. Prenter. "Higher order methods for convection-diffusion problems." Computers & Fluids 13, no. 2 (January 1985): 157–76. http://dx.doi.org/10.1016/0045-7930(85)90023-4.

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41

Luo, C., B. Z. Dlugogorski, B. Moghtaderi, and E. M. Kennedy. "Modified exponential schemes for convection–diffusion problems." Communications in Nonlinear Science and Numerical Simulation 13, no. 2 (March 2008): 369–79. http://dx.doi.org/10.1016/j.cnsns.2006.03.014.

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42

Li, Yuxia. "Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems." East Asian Journal on Applied Mathematics 10, no. 1 (June 2020): 158–80. http://dx.doi.org/10.4208/eajam.231118.240619.

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43

Patel, M. K., N. C. Markatos, and M. Cross. "Method of reducing false-diffusion errors in convection—diffusion problems." Applied Mathematical Modelling 9, no. 4 (August 1985): 302–6. http://dx.doi.org/10.1016/0307-904x(85)90069-1.

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44

John, V., J. M. Maubach, and L. Tobiska. "Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems." Numerische Mathematik 78, no. 2 (December 1, 1997): 165–88. http://dx.doi.org/10.1007/s002110050309.

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45

Linß, Torsten. "Anisotropic meshes and streamline-diffusion stabilization for convection-diffusion problems." Communications in Numerical Methods in Engineering 21, no. 10 (April 19, 2005): 515–25. http://dx.doi.org/10.1002/cnm.764.

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46

Unno, Wasaburo. "Problems of Solar Convection." Symposium - International Astronomical Union 142 (1990): 39–44. http://dx.doi.org/10.1017/s0074180900087672.

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Abstract:

Kinetic energy of convection is transported inwards in the main body of convection zone. The temperature gradient becomes super-radiative at the top of the overshooting zone. These two effects make the solar equilibrium model much less sensitive to the assumed mixing length in Xiong's eddy diffusion theory. Observed brightening of downflow at high level in the surface region over intergranular lanes seems to be consistent with the overshooting model. Momentum transport by convective motion is shown to be crucial in pushing down magnetic flux tubes against buoyancy. Also, subadiabatic layers are possibly formed temporarily in the middle of the convection zone, exciting oscillations and generating chaotic motions.

47

Wang, Jufeng, and Fengxin Sun. "A Hybrid Variational Multiscale Element-Free Galerkin Method for Convection-Diffusion Problems." International Journal of Applied Mechanics 11, no. 07 (August 2019): 1950063. http://dx.doi.org/10.1142/s1758825119500637.

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By coupling the dimension splitting method (DSM) and the variational multiscale element-free Galerkin (VMEFG) method, a hybrid variational multiscale element-free Galerkin (HVMEFG) method is developed for the two-dimensional convection-diffusion problems. In the HVMEFG method, the two-dimensional problem is converted into a battery of one-dimensional problems by the DSM. Combining the non-singular improved interpolating moving least-squares (IIMLS) method, the VMEFG method is used to obtain the discrete equations of the one-dimensional problems on the splitting plane. Then, final discretized equations of the entire convection-diffusion problems are assembled by the IIMLS method. The HVMEFG method has high accuracy and efficiency. Numerical examples show that the HVMEFG method can obtain non-oscillating solutions and has higher efficiency and accuracy than the EFG and VMEFG methods for convection-diffusion problems.

48

Nguyen, Tran Ba Dinh, Hoang Son Nguyen, and Duc-Huynh Phan. "A Novel Least-Squares Level Set Method by Using Polygonal Elements." Journal of Technical Education Science, no. 72A (October 28, 2022): 45–53. http://dx.doi.org/10.54644/jte.72a.2022.1232.

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In this study, we apply an artificial viscosity method to convert an unsteady level set (LS) convection equation into an unsteady LS convection-diffusion transport equation to stabilize the numerical solution of the convection term. Then a novel least-square polygonal finite element method is used to solve an unsteady LS convection-diffusion problem. The least-squares method provided good mathematical properties such as natural numerical diffusion and the positive definite symmetry of the resulting algebraic systems for the convection-diffusion and re-initialization equations. The proposed method is evaluated numerically in two different benchmark problems: a rigid body rotation of Zalesak’s disk, and a time-reversed single-vortex flow. In comparison with conventional triangular (T3) and quadrilateral (Q4) elements, polygonal elements are capable of providing greater flexibility in mesh generation for complicated problems as well as more accurate in solving the LS equations. In addition, the numerical results are also compared with the results which obtained from essentially non-oscillatory type formulations and particle LS methods. The results show that the proposed method completely matches the previously published results.

49

Llorente, Ignacio M., Manuel Prieto-Matı́as, and Boris Diskin. "A parallel multigrid solver for 3D convection and convection–diffusion problems." Parallel Computing 27, no. 13 (December 2001): 1715–41. http://dx.doi.org/10.1016/s0167-8191(01)00115-6.

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50

He, Qian, Wenxin Du, Feng Shi, and Jiaping Yu. "A fast method for solving time-dependent nonlinear convection diffusion problems." Electronic Research Archive 30, no. 6 (2022): 2165–82. http://dx.doi.org/10.3934/era.2022109.

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Abstract:

<abstract><p>In this paper, a fast scheme for solving unsteady nonlinear convection diffusion problems is proposed and analyzed. At each step, we firstly isolate a nonlinear convection subproblem and a linear diffusion subproblem from the original problem by utilizing operator splitting. By Taylor expansion, we explicitly transform the nonlinear convection one into a linear problem with artificial inflow boundary conditions associated with the nonlinear flux. Then a multistep technique is provided to relax the possible stability requirement, which is due to the explicit processing of the convection problem. Since the self-adjointness and coerciveness of diffusion subproblems, there are so many preconditioned iterative solvers to get them solved with high efficiency at each time step. When using the finite element method to discretize all the resulting subproblems, the major stiffness matrices are same at each step, that is the reason why the unsteady nonlinear systems can be computed extremely fast with the present method. Finally, in order to validate the effectiveness of the present scheme, several numerical examples including the Burgers type and Buckley-Leverett type equations, are chosen as the numerical study.</p></abstract>