Differential quadrature methodfor some diffusion-reaction problems

• Autorzy: Szukiewicz Mirosław K.

Identyfikatory

DOI

10.24425/cpe.2019.130219

• Języki publikacji: EN

Abstrakty

EN

In the paper, differential quadrature method (DQM) is used to find numerical solutions of reaction-diffusion equations with different boundary conditions. The DQM-method changes the reaction-diffusion equation (ordinary differential equation) into a system of algebraic equations. The obtainedsystem is solved using built-in procedures of Maple®(Computer Algebra System-type program).Calculations were performed with Maple®program. The test problems include reaction-diffusionequation applied in heterogeneous catalysis. The method can be employed even in relatively hard tasks(e.g. ill-conditioned, free boundary problems).

Słowa kluczowe

EN

numerical algorithm; boundary value problem; reaction-diffusion equation

PL

algorytm numeryczny; wartość graniczna; równanie dyfuzji reakcyjnej

• Wydawca: Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk
• Czasopismo: Chemical and Process Engineering
• Rocznik: 2020
• Tom: Vol. 41, nr 1
• Strony: 3--11
• Opis fizyczny: Bibliogr. 15 poz., tab., rys.

Twórcy

autor

Szukiewicz Mirosław K.

• Rzeszów University of Technology, Department of Chemical and Process Engineering,al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland

Bibliografia

• 1. Andreev V.V., 2013. Formation of a “dead zone” in porous structures during processes that proceeding understeady-state and unsteady-state conditions.Rev. J. Chem., 3, 239–269. DOI: 10.1134/S2079978013030011.
• 2. Bellman R., Kashef B.G., Casti J., 1972. Differential quadrature: A technique for the rapid solution of nonlinearpartial differential equations.J. Comput. Phys., 10, 40–52. DOI: 10.1016/0021-9991(72)90089-7.
• 3. Campo A., Lacoa U., 2014. Adaptation of the Method Of Lines (MOL) to the MATLAB code for the analysis ofthe Stefan problem.WSEAS Trans. Heat Mass Transfer, 9, 19–26.
• 4. Chen W., 1996.Differential quadrature method and its applications in engineering – applying special matrixproduct to nonlinear computations and analysis. PhD Thesis, Mechatronic Control and Automation Departmentof Mechanical Engineering, Shanghai Jiao Tong University. Differential quadrature method for some diffusion-reaction problems
• 5. Davis M.E., 1984.Numerical Methods and Modeling for Chemical Engineers. Wiley, New York.
• 6. Jiwari R., Singh S., Kumar A., 2017. Numerical simulation to capture the pattern formation of coupled reaction-diffusion models.Chaos, Solitons Fractals, 103, 422–439. DOI: 10.1016/j.chaos.2017.06.023.
• 7. Johansson B.T., Lesnic D., Reeve T., 2014. A meshless method for an inverse two-phase one-dimensional nonlinearStefan problem. Math. Comput. Simul, 101, 61–77. DOI: 10.1016/j.matcom.2014.03.004.
• 8. Lee J.K., Ko J.B., Kim D.H., 2004. Methanol steam reforming over Cu/ZnO/Al2O3catalyst: kinetics and effective-ness factor.Appl. Cat. A, 278, 25–35. DOI: 10.1016/j.apcata.2004.09.022.
• 9. Meral G., Tezer-Sezgin M., 2011. The comparison between the DRBEM and DQM solution of nonlinear reaction–diffusion equation.Commun. Nonlinear Sci. Numer. Simulat., 16, 3990–4005. DOI: 10.1016/j.cnsns.2011.02.008.
• 10. Mitchell S.L., Vynnycky M., 2014. On the numerical solution of two-phase Stefan problems with heat-flux boundaryconditions.J. Comput. Appl. Math., 264, 49–64. DOI: 10.1016/j.cam.2014.01.003.
• 11. Salah M., Amer R. M., Matbuly M. S., 2014. The differential quadrature solution of reaction-diffusion equationusing explicit and implicit numerical schemes.Appl. Math., 5, 327–336. DOI: 10.4236/am.2014.53033.
• 12. Szukiewicz M., Chmiel-Szukiewicz E., Kaczmarski K., Szałek A., 2019. Dead zone for hydrogenation of propylenereaction carried out on commercial catalyst pellets.Open Chemistry, 17, 295–301. DOI: 10.1515/chem-2019-0037.
• 13. Trefethen L.N.,Spectral methods in MATLAB. Philadelphia, SIAM, 2000.
• 14. Villadsen J., Michelsen M.,Solution of differential equation models by polynomial approximation. EnglewoodCliffs, N.J., Prentice-Hall, 1978.
• 15. York R.L., Bratlie K.M., Hile R.L., Jang L.K., 2011. Dead zones in porous catalysts: Concentration profiles andefficiency factors.Catal. Today, 160, 204–212. DOI: 10.1016/j.cattod.2010.06.022.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).