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Journal articles on the topic 'Reaction-convection-diffusion equations'

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Author: Grafiati

Published: 14 March 2023

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1

El-Wakil, S. A., A. Elhanbaly, and M. A. Abdou. "On the Diffusion-Convection-Reaction Equations." Physica Scripta 60, no. 3 (September 1, 1999): 207–10. http://dx.doi.org/10.1238/physica.regular.060a00207.

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2

de Pablo, Arturo, and Ariel Sánchez. "Global Travelling Waves in Reaction–Convection–Diffusion Equations." Journal of Differential Equations 165, no. 2 (August 2000): 377–413. http://dx.doi.org/10.1006/jdeq.2000.3781.

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3

Iliescu, Traian, and Zhu Wang. "Variational multiscale proper orthogonal decomposition: Convection-dominated convection-diffusion-reaction equations." Mathematics of Computation 82, no. 283 (March 18, 2013): 1357–78. http://dx.doi.org/10.1090/s0025-5718-2013-02683-x.

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4

Giere, Swetlana, Traian Iliescu, Volker John, and David Wells. "SUPG reduced order models for convection-dominated convection–diffusion–reaction equations." Computer Methods in Applied Mechanics and Engineering 289 (June 2015): 454–74. http://dx.doi.org/10.1016/j.cma.2015.01.020.

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5

Choudhury, A. H. "Wavelet Method for Numerical Solution of Parabolic Equations." Journal of Computational Engineering 2014 (February 27, 2014): 1–12. http://dx.doi.org/10.1155/2014/346731.

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We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.

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6

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.

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7

Lu, Yunguang, and Willi Jäger. "On Solutions to Nonlinear Reaction–Diffusion–Convection Equations with Degenerate Diffusion." Journal of Differential Equations 170, no. 1 (February 2001): 1–21. http://dx.doi.org/10.1006/jdeq.2000.3800.

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8

Ei, Shin-Ichiro. "The effect of nonlocal convection on reaction-diffusion equations." Hiroshima Mathematical Journal 17, no. 2 (1987): 281–307. http://dx.doi.org/10.32917/hmj/1206130067.

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9

Geiser, Jürgen, Jose L. Hueso, and Eulalia Martínez. "Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations." Mathematics 8, no. 3 (February 25, 2020): 302. http://dx.doi.org/10.3390/math8030302.

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This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection–diffusion–reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers’ and Maxwell–Stefan diffusion equations.

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10

Sarrico, C. O. R. "New singular travelling waves for convection–diffusion–reaction equations." Journal of Physics A: Mathematical and Theoretical 53, no. 15 (March 26, 2020): 155202. http://dx.doi.org/10.1088/1751-8121/ab7c1d.

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11

RODRIGO, M., and M. MIMURA. "ON SOME CLASSES OF LINEARIZABLE REACTION-CONVECTION-DIFFUSION EQUATIONS." Analysis and Applications 02, no. 01 (January 2004): 11–19. http://dx.doi.org/10.1142/s0219530504000266.

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In this paper, we consider the class of equations ut=[F(x,u)ux+G(x,u)]x+H(x,u). Using hodograph and dependent variable transformations, we determine sufficient conditions on F, G, and H such that this equation is linearizable. We also derive a general quasilinear equation, which includes the Clarkson–Fokas–Ablowitz equation (SIAM J. Appl. Math.49 (1989), 1188–1209), that can be transformed into semilinear form.

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12

Kennedy, Christopher A., and Mark H. Carpenter. "Additive Runge–Kutta schemes for convection–diffusion–reaction equations." Applied Numerical Mathematics 44, no. 1-2 (January 2003): 139–81. http://dx.doi.org/10.1016/s0168-9274(02)00138-1.

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13

Lou, Bendong. "Singular Limits of Spatially Inhomogeneous Convection-reaction-diffusion Equations." Journal of Statistical Physics 129, no. 3 (September 13, 2007): 509–16. http://dx.doi.org/10.1007/s10955-007-9400-3.

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14

Indekeu, Joseph O., and Ruben Smets. "Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations." Journal of Physics A: Mathematical and Theoretical 50, no. 31 (July 6, 2017): 315601. http://dx.doi.org/10.1088/1751-8121/aa7a93.

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15

Hernández, H., T. J. Massart, R. H. J. Peerlings, and M. G. D. Geers. "A stabilization technique for coupled convection-diffusion-reaction equations." International Journal for Numerical Methods in Engineering 116, no. 1 (July 25, 2018): 43–65. http://dx.doi.org/10.1002/nme.5914.

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16

O' Riordan, Eugene, Maria L. Pickett, and Georgii I. Shishkin. "Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes." Computational Methods in Applied Mathematics 3, no. 3 (2003): 424–42. http://dx.doi.org/10.2478/cmam-2003-0028.

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AbstractIn this paper, parameter - uniform numerical methods for singularly perturbed ordinary differential equations containing two small parameters are studied.Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

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17

ZHANG, WEN. "DIFFUSIVE EFFECTS ON A CATALYTIC SURFACE REACTION: AN INITIAL BOUNDARY VALUE PROBLEM IN REACTION-DIFFUSION-CONVECTION EQUATIONS." International Journal of Bifurcation and Chaos 03, no. 01 (February 1993): 79–95. http://dx.doi.org/10.1142/s0218127493000052.

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A bimolecular catalytic surface reaction is extended to include diffusion which yields mobilized coverage on the surface. We consider the reaction occurring in a tubular reactor with a convection flow where the reactants also diffuse. An initial boundary value problem in one-dimensional reaction-diffusion-convection equations is used in describing the model. We combine singular perturbation analysis with numerical simulations in studying the solution behavior in parameter space. We track the reaction front and the cause of period-2 oscillations. Compared with the case of having no surface diffusion, we observe regular oscillations instead of irregular oscillations. Compared with the nondiffusive nonconvective model, we obtain rich spatiotemporal patterns including stationary, oscillatory reaction fronts and multiple steady states.

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18

Berti, Diego, Andrea Corli, and Luisa Malaguti. "Diffusion–convection reaction equations with sign-changing diffusivity and bistable reaction term." Nonlinear Analysis: Real World Applications 67 (October 2022): 103579. http://dx.doi.org/10.1016/j.nonrwa.2022.103579.

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19

Corli, Andrea, Luisa Malaguti, and Elisa Sovrano. "Wavefront solutions to reaction-convection equations with Perona-Malik diffusion." Journal of Differential Equations 308 (January 2022): 474–506. http://dx.doi.org/10.1016/j.jde.2021.09.041.

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20

Zhong, Liuqiang, Yue Xuan, and Jintao Cui. "Two-grid discontinuous Galerkin method for convection–diffusion–reaction equations." Journal of Computational and Applied Mathematics 404 (April 2022): 113903. http://dx.doi.org/10.1016/j.cam.2021.113903.

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21

Seymen, Zahire, and Bülent Karasözen. "Optimal boundary control for time-dependent diffusion-convection-reaction equations." International Journal of Mathematical Modelling and Numerical Optimisation 4, no. 3 (2013): 282. http://dx.doi.org/10.1504/ijmmno.2013.056543.

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22

Simon, K., and L. Tobiska. "Local projection stabilization for convection–diffusion–reaction equations on surfaces." Computer Methods in Applied Mechanics and Engineering 344 (February 2019): 34–53. http://dx.doi.org/10.1016/j.cma.2018.09.031.

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23

Liu, Qingfang, Yanren Hou, Lei Ding, and Qingchang Liu. "A Stabilized Galerkin Scheme for the Convection-Diffusion-Reaction Equations." Acta Applicandae Mathematicae 130, no. 1 (August 23, 2013): 115–34. http://dx.doi.org/10.1007/s10440-013-9840-5.

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24

Kaya, Adem. "Finite difference approximations of multidimensional unsteady convection–diffusion–reaction equations." Journal of Computational Physics 285 (March 2015): 331–49. http://dx.doi.org/10.1016/j.jcp.2015.01.024.

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25

Serov, M. I., T. O. Karpaliuk, O. G. Pliukhin, and I. V. Rassokha. "Systems of reaction–convection–diffusion equations invariant under Galilean algebras." Journal of Mathematical Analysis and Applications 422, no. 1 (February 2015): 185–211. http://dx.doi.org/10.1016/j.jmaa.2014.08.018.

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26

El-Wakil, S. A., M. A. Abdou, and A. Elhanbaly. "Adomian decomposition method for solving the diffusion–convection–reaction equations." Applied Mathematics and Computation 177, no. 2 (June 2006): 729–36. http://dx.doi.org/10.1016/j.amc.2005.09.105.

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27

Hai, Doan Duy, and Atsushi Yagi. "Rosenbrock strong stability-preserving methods for convection–diffusion–reaction equations." Japan Journal of Industrial and Applied Mathematics 31, no. 2 (May 15, 2014): 401–17. http://dx.doi.org/10.1007/s13160-014-0143-7.

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28

Kaya, A. "A finite difference scheme for multidimensional convection–diffusion–reaction equations." Computer Methods in Applied Mechanics and Engineering 278 (August 2014): 347–60. http://dx.doi.org/10.1016/j.cma.2014.06.002.

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29

Hou, Qingzhi, Jiaru Liu, Jijian Lian, and Wenhuan Lu. "A Lagrangian Particle Algorithm (SPH) for an Autocatalytic Reaction Model with Multicomponent Reactants." Processes 7, no. 7 (July 3, 2019): 421. http://dx.doi.org/10.3390/pr7070421.

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For the numerical simulation of convection-dominated reacting flow problems governed by convection-reaction equations, grids-based Eulerian methods may cause different degrees of either numerical dissipation or unphysical oscillations. In this paper, a Lagrangian particle algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for convection-reaction equations and is applied to an autocatalytic reaction model with multicomponent reactants. Four typical Eulerian methods are also presented for comparison, including the high-resolution technique with the Superbee flux limiter, which has been considered to be the most appropriate technique for solving convection-reaction equations. Numerical results demonstrated that when comparing with traditional first- and second-order schemes and the high-resolution technique, the present Lagrangian particle algorithm has better numerical accuracy. It can correctly track the moving steep fronts without suffering from numerical diffusion and spurious oscillations.

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30

Pavelchuk, Anna Vladimirovna, and Anna Gennadievna Maslovskaya. "MODIFIED FINITE-DIFFERENCE SCHEME FOR SOLVING ONE CLASS OF CONVECTION-REACTION-DIFFUSION PROBLEMS." Messenger AmSU, no. 93 (2021): 7–14. http://dx.doi.org/10.22250/jasu.93.2.

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The paper reviews approaches to the construction of finite-difference methods for solving time-dependent diffusion equations and transport equations. A modified computational scheme for solving a semilinear multidimensional equation of the «reaction – diffusion – convection» type is presented. The hybrid computational scheme is based on the alternating directions method and the Robert-Weiss scheme.

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31

Junk, Michael, and Zhaoxia Yang. "L2Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations." Communications in Computational Physics 17, no. 5 (May 2015): 1225–45. http://dx.doi.org/10.4208/cicp.2014.m369.

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AbstractCombining asymptotic analysis and weightedL2stability estimates, the convergence of lattice Boltzmann methods for the approximation of 1D convection-diffusion-reaction equations is proved. Unlike previous approaches, the proof does not require transformations to equivalent macroscopic equations.

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32

John, Volker, and Ellen Schmeyer. "Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion." Computer Methods in Applied Mechanics and Engineering 198, no. 3-4 (December 2008): 475–94. http://dx.doi.org/10.1016/j.cma.2008.08.016.

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33

CARETA, A., F. SAGUÉS, and J. M. SANCHO. "DYNAMICS OF REACTION-DIFFUSION INTERFACES UNDER STOCHASTIC CONVECTION: PRELIMINARY RESULTS." International Journal of Bifurcation and Chaos 04, no. 05 (October 1994): 1329–31. http://dx.doi.org/10.1142/s0218127494001015.

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Some preliminary results to illustrate the effect of turbulent convection on the dynamics of physicochemical systems incorporating reaction, diffusion and convection of chemical species are given. The whole approach rests on the use of stochastic differential equations with spatiotemporal correlated noise. In particular, it is shown how the propagation velocity of a chemically reacting front can be enhanced due to the fluid motion.

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34

Zheng, Si Ning. "Weakly invariant regions for reaction—diffusion systems and applications." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 5 (October 2000): 1165–80. http://dx.doi.org/10.1017/s0308210500000627.

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The important theory of invariant regions in reaction-diffusion equations has only restricted applications because of its strict requirements on both the reaction terms and the regions. The concept of weakly invariant regions was introduced by us to admit wider reaction-diffusion systems. In this paper we first extend the L∞ estimate technique of semilinear parabolic equations of Rothe to the more general case with convection terms, and then propose more precise criteria for the bounded weakly invariant regions. We illustrate, by three model examples, that they are very convenient for establishing the global existence of solutions for reaction-diffusion systems, especially those from ecology and chemical processes.

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35

Carstea, A. S. "Reaction–diffusion–convection equations in two spatial dimensions; continuous and discrete dynamics." Modern Physics Letters B 35, no. 10 (February 18, 2021): 2150186. http://dx.doi.org/10.1142/s0217984921501864.

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In this paper, we investigate some two-dimensional (with respect to spatial independent variables) reaction–diffusion–convection equations with various nonlinear (reaction) terms. Using Hirota bilinear formalism with a free auxiliary function, we obtain kink solutions and many spatio-temporal discretizations having birational form.

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36

Abdulle, Assyr, and Giacomo Rosilho de Souza. "A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations." Journal of Computational Physics 451 (February 2022): 110894. http://dx.doi.org/10.1016/j.jcp.2021.110894.

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37

Berti, Diego, Andrea Corli, and Luisa Malaguti. "Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 66 (2020): 1–34. http://dx.doi.org/10.14232/ejqtde.2020.1.66.

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38

Liu, Bochao, and Chengjian Zhang. "A spectral Galerkin method for nonlinear delay convection–diffusion–reaction equations." Computers & Mathematics with Applications 69, no. 8 (April 2015): 709–24. http://dx.doi.org/10.1016/j.camwa.2015.02.027.

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39

Cherniha, Roman, Mykola Serov, and Inna Rassokha. "Lie symmetries and form-preserving transformations of reaction–diffusion–convection equations." Journal of Mathematical Analysis and Applications 342, no. 2 (June 2008): 1363–79. http://dx.doi.org/10.1016/j.jmaa.2008.01.011.

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40

Serov, Mykola I., and Inna V. Rassokha. "Galilei’s relativity principle for a system of reaction-convection-diffusion equations." Journal of Mathematical Sciences 194, no. 5 (September 28, 2013): 539–56. http://dx.doi.org/10.1007/s10958-013-1549-5.

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41

Bobisud, L. E., D. O'Regan, and W. D. Royalty. "Steady-state reaction-diffusion-convection equations: dead cores and singular perturbations." Nonlinear Analysis: Theory, Methods & Applications 11, no. 4 (January 1987): 527–38. http://dx.doi.org/10.1016/0362-546x(87)90069-1.

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42

Tezduyar, T. E., and Y. J. Park. "Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations." Computer Methods in Applied Mechanics and Engineering 59, no. 3 (December 1986): 307–25. http://dx.doi.org/10.1016/0045-7825(86)90003-4.

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43

Sun, Xiaodi, and Michael J. Ward. "Metastability and pinning for convection-diffusion-reaction equations in thin domains." Methods and Applications of Analysis 6, no. 4 (1999): 451–76. http://dx.doi.org/10.4310/maa.1999.v6.n4.a3.

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44

Hernández, H., T. J. Massart, R. H. J. Peerlings, and M. G. D. Geers. "Stabilization of coupled convection–diffusion-reaction equations for continuum dislocation transport." Modelling and Simulation in Materials Science and Engineering 27, no. 5 (May 16, 2019): 055009. http://dx.doi.org/10.1088/1361-651x/ab1b84.

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45

Uzunca, Murat, Bülent Karasözen, and Murat Manguoğlu. "Adaptive discontinuous Galerkin methods for non-linear diffusion–convection–reaction equations." Computers & Chemical Engineering 68 (September 2014): 24–37. http://dx.doi.org/10.1016/j.compchemeng.2014.05.002.

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46

Chen, Gang, Minfu Feng, and Xiaoping Xie. "A robust WG finite element method for convection–diffusion–reaction equations." Journal of Computational and Applied Mathematics 315 (May 2017): 107–25. http://dx.doi.org/10.1016/j.cam.2016.10.029.

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47

Cherniha, Roman, and Oleksii Pliukhin. "Symmetries and solutions of reaction-diffusion-convection equations with power diffusivities." PAMM 7, no. 1 (December 2007): 2040065–66. http://dx.doi.org/10.1002/pamm.200700744.

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48

Cheng, Heng, Zebin Xing, and Yan Liu. "The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients." Mathematics 11, no. 3 (February 3, 2023): 770. http://dx.doi.org/10.3390/math11030770.

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In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape function. For the governing equation of 3D convection-diffusion-reaction problems, we can derive the corresponding equivalent functional; then, the essential boundary conditions are imposed by applying the penalty method; thus, the equivalent integral weak form is obtained. By introducing the IMLS approximation, we can derive the final solved linear equations of the convection-diffusion-reaction problem. In numerical examples, the scale parameter and the penalty factor of the IEFG method for such problems are discussed, the convergence is proved numerically, and the calculation efficiency of the IEFG method are verified by four numerical examples.

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49

Di Francesco, Marco, Klemens Fellner, and Peter A. Markowich. "The entropy dissipation method for spatially inhomogeneous reaction–diffusion-type systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2100 (August 21, 2008): 3273–300. http://dx.doi.org/10.1098/rspa.2008.0214.

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We study the long-time asymptotics of reaction–diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion–convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction–diffusion–convection system arising in solid-state physics as a paradigm for general nonlinear systems.

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50

Linss, T., and M. Stynes. "Numerical Solution of Systems of Singularly Perturbed Differential Equations." Computational Methods in Applied Mathematics 9, no. 2 (2009): 165–91. http://dx.doi.org/10.2478/cmam-2009-0010.

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AbstractA survey is given of current research into the numerical solution of timeindependent systems of second-order differential equations whose diffusion coefficients are small parameters. Such problems are in general singularly perturbed. The equations in these systems may be coupled through their reaction and/or convection terms. Only numerical methods whose accuracy is guaranteed for all values of the diffusion parameters are considered here. Some new unifying results are also presented.

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