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Hernández Marulanda, A. F., & Gaviria Posada, L. J. (2020). Solución de la ecuación de convección difusión mediante las funciones de base radial multicuádricas. Ingenierías USBmed, 11(2), 48–53. https://doi.org/10.21500/20275846.4727
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Abstract
En este paper se propone un algoritmo computacional que resuelve la ecuación de convección difusión unidimensional estacionaria, utilizando un método numérico basado en las funciones de base radial (RBF). Para la aplicación de este algoritmo es necesaria la generación de diferentes valores del número de Peclet para obtener soluciones gráficas, en donde se comparó con la solución analítica reportada por Patankar.
References
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V. Aswin, A. Awasthi y C. Anu, «A comparative study of numerical schemes for convection-diffusion equation,» International Conference on Computational Heat and Mass Transfer-2015, nº 127, pp. 621-627, 2015.
J. Biazar y . M. Bagher Mehrlatifan, «A Compact Finite Difference Scheme for Reaction-convection-diffusion Equation,» Chiang Mai Journal of Science, vol. 3, nº 45, pp. 1559-1568, 2017.
P. Assari y M. Dehghan, «A meshless Galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions,» Journal of Computational and Applied Mathematics, vol. 333, pp. 362-381, 2018.
J. M. Granados, C. A. Bustamante, H. Power y W. F. Florez, «A global Stokes method of approximated particular solutions for unsteady two-dimensional Navier–Stokes system of equations,» International Journal of Computer Mathematics, nº 94, pp. 1515-1541, 2016.
B. Sarlet y R. Vertnik, «Meshfree explicit locl radial basis function collocation method for diffusion problems,» Comput. Math. Appl, nº 51, pp. 1269-1282, 2006.
E. Kansa, «Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics - iL solutions to parabolic, hyperbolic and elliptic partial differential equations,» Comput. Math. Appl, nº 19, pp. 147-161, 1990.
S. Scott A, «Radial basis function approximation methods with extended precision,» Engineering Analysis with Boundary Elements, vol. 35, pp. 68-76, 2011.
W. F. Forez, H. Power y F. Chejne, «Conservative interpolation for the boundary integral solutio of the navier-stokes equations,» Computational Mechanics, nº 26, pp. 507-513, 2000.
G. Fasshauer, Solving partial differential equations by collocation with radial basis functions, A. Le Méhauté, C. Rabut, L.L. Schumaker, Surface Fitting and Multiresolution Methods, Vanderbilt University Press, 1997.
C. Bustamante, H. Power y W. Florez, «A global meshless collocation particular solution method for solving the two dimensional Navier Stokes system of equations,» Computers and Mathematics with Applications, nº 65, pp. 1929-1955, 2013.
G. Lima, V. Ferreira, E. Cirilo, A. Castelo, M. Candezano, I. Tasso, D. Sano y L. Scalvi, «A continuously differentiable upwinding scheme for the simulation of fluid flow problems,» Applied Mathematics and Computation, nº 218, pp. 8614-8633, 2012.
T. Ghaffar, M. Yousaf y S. Qamar, «Numerical solution of special ultra-relativistic Euler equations using central upwind scheme,» Results in Physics, nº 9, pp. 1161-1169, 2018.
M. Saqib, S. Hasnain y D. Suleiman Mashat, «Computational Solutions of Two Dimensional Convection Diffusion Equation Using Crank-Nicolson and Time Efficient ADI,» American Journal of Computational Mathematics, nº 7, pp. 208-227, 2017.
S. Patankar y D. Spalding, «A calculation procedure for heat, mass and momentum trnasfer in three-dimensional parabolic flows,» Int.J.Heat Mass Transfer, nº 15, pp. 1787-1806, 1972.
S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, 1980.
W. Chen y M. Tanaka, «A meshless, integration-free, and boundary - only RBF technique,» Comput. Math. Appl, nº 43, pp. 379-391, 2002.
R. Vertnik y B. Sarlet, «Meshless local radial basis function collocation for convective-dissusive solid - liquid phase change problems,» Int. J. Numer. Methods Heat fluid Flow, vol. 16, nº 5, pp. 617-640, 2006.
A. F. Hernández Marulanda, W. F. Flórez Escobar y J. J. Bustamante Osorno, «Simulación de interacción fluido-estructura en la red vascular utilizando el método de elementos de frontera (BEM),» Revista Ingeniería Biomédica, vol. 13, nº 25, pp. 53-62, 2019.
A. Appadu, J. Djoko y H. Gidey, «A computational study of three numerical methods for some advection-diffusion problems,» Applied Mathematics, vol. 272, nº 3, pp. 629-647, 2016.
M. McGinty y G. Pontrelli, «A general model of coupled drug release and tissue absorption for drug,» Journal of Controlled Release, nº 217, pp. 327-336, 2015.
W. Chen, . Y. Linjuan y . S. Hongguang , «Fractional diffusion equations by the Kansa method,» Computers and Mathematics with Applications, nº 59, pp. 1614-1620, 2010.
V. Aswin, A. Awasthi y C. Anu, «A comparative study of numerical schemes for convection-diffusion equation,» International Conference on Computational Heat and Mass Transfer-2015, nº 127, pp. 621-627, 2015.
J. Biazar y . M. Bagher Mehrlatifan, «A Compact Finite Difference Scheme for Reaction-convection-diffusion Equation,» Chiang Mai Journal of Science, vol. 3, nº 45, pp. 1559-1568, 2017.
P. Assari y M. Dehghan, «A meshless Galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions,» Journal of Computational and Applied Mathematics, vol. 333, pp. 362-381, 2018.
J. M. Granados, C. A. Bustamante, H. Power y W. F. Florez, «A global Stokes method of approximated particular solutions for unsteady two-dimensional Navier–Stokes system of equations,» International Journal of Computer Mathematics, nº 94, pp. 1515-1541, 2016.
B. Sarlet y R. Vertnik, «Meshfree explicit locl radial basis function collocation method for diffusion problems,» Comput. Math. Appl, nº 51, pp. 1269-1282, 2006.
E. Kansa, «Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics - iL solutions to parabolic, hyperbolic and elliptic partial differential equations,» Comput. Math. Appl, nº 19, pp. 147-161, 1990.
S. Scott A, «Radial basis function approximation methods with extended precision,» Engineering Analysis with Boundary Elements, vol. 35, pp. 68-76, 2011.
W. F. Forez, H. Power y F. Chejne, «Conservative interpolation for the boundary integral solutio of the navier-stokes equations,» Computational Mechanics, nº 26, pp. 507-513, 2000.
G. Fasshauer, Solving partial differential equations by collocation with radial basis functions, A. Le Méhauté, C. Rabut, L.L. Schumaker, Surface Fitting and Multiresolution Methods, Vanderbilt University Press, 1997.
C. Bustamante, H. Power y W. Florez, «A global meshless collocation particular solution method for solving the two dimensional Navier Stokes system of equations,» Computers and Mathematics with Applications, nº 65, pp. 1929-1955, 2013.
G. Lima, V. Ferreira, E. Cirilo, A. Castelo, M. Candezano, I. Tasso, D. Sano y L. Scalvi, «A continuously differentiable upwinding scheme for the simulation of fluid flow problems,» Applied Mathematics and Computation, nº 218, pp. 8614-8633, 2012.
T. Ghaffar, M. Yousaf y S. Qamar, «Numerical solution of special ultra-relativistic Euler equations using central upwind scheme,» Results in Physics, nº 9, pp. 1161-1169, 2018.
M. Saqib, S. Hasnain y D. Suleiman Mashat, «Computational Solutions of Two Dimensional Convection Diffusion Equation Using Crank-Nicolson and Time Efficient ADI,» American Journal of Computational Mathematics, nº 7, pp. 208-227, 2017.
S. Patankar y D. Spalding, «A calculation procedure for heat, mass and momentum trnasfer in three-dimensional parabolic flows,» Int.J.Heat Mass Transfer, nº 15, pp. 1787-1806, 1972.
S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, 1980.
W. Chen y M. Tanaka, «A meshless, integration-free, and boundary - only RBF technique,» Comput. Math. Appl, nº 43, pp. 379-391, 2002.
R. Vertnik y B. Sarlet, «Meshless local radial basis function collocation for convective-dissusive solid - liquid phase change problems,» Int. J. Numer. Methods Heat fluid Flow, vol. 16, nº 5, pp. 617-640, 2006.
A. F. Hernández Marulanda, W. F. Flórez Escobar y J. J. Bustamante Osorno, «Simulación de interacción fluido-estructura en la red vascular utilizando el método de elementos de frontera (BEM),» Revista Ingeniería Biomédica, vol. 13, nº 25, pp. 53-62, 2019.
A. Appadu, J. Djoko y H. Gidey, «A computational study of three numerical methods for some advection-diffusion problems,» Applied Mathematics, vol. 272, nº 3, pp. 629-647, 2016.
M. McGinty y G. Pontrelli, «A general model of coupled drug release and tissue absorption for drug,» Journal of Controlled Release, nº 217, pp. 327-336, 2015.
W. Chen, . Y. Linjuan y . S. Hongguang , «Fractional diffusion equations by the Kansa method,» Computers and Mathematics with Applications, nº 59, pp. 1614-1620, 2010.
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