Time-centered split method for implicit discretization of unsteady advection problems / Shipeng Fu in Journal of engineering mechanics, Vol. 135 N° 4 (Avril 2009)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 135 N° 4 (Avril 2009) . - pp. 256-264 Titre : Time-centered split method for implicit discretization of unsteady advection problems Type de document : texte imprimé Auteurs : Shipeng Fu, Auteur ; Hodges, Ben R., Auteur Article en page(s) : pp. 256-264 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Computational fluid dynamics technique Finite difference method Numerical methods Nonlinear systems. Résumé : A new method for implicit solution of unsteady nonlinear advection equations is presented. This time-centered split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically nonlinear coupled equations for any number of variables. The TCS algorithm is compared to other nonlinear solution methods (local linearization, Picard iteration, and Newton iteration) and applied to the Crank-Nicolson discretization of the one-dimensional Burgers' equation. The temporal accuracy and practical stability of the method is confirmed using an unsteady flow test case with an analytical solution. The method is shown to require computational effort similar to local linearization, but does not require discrete computation of a functional Jacobian for solution. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...] [article] Time-centered split method for implicit discretization of unsteady advection problems [texte imprimé] / Shipeng Fu, Auteur ; Hodges, Ben R., Auteur . - pp. 256-264. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 135 N° 4 (Avril 2009) . - pp. 256-264 Mots-clés : Computational fluid dynamics technique Finite difference method Numerical methods Nonlinear systems. Résumé : A new method for implicit solution of unsteady nonlinear advection equations is presented. This time-centered split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically nonlinear coupled equations for any number of variables. The TCS algorithm is compared to other nonlinear solution methods (local linearization, Picard iteration, and Newton iteration) and applied to the Crank-Nicolson discretization of the one-dimensional Burgers' equation. The temporal accuracy and practical stability of the method is confirmed using an unsteady flow test case with an analytical solution. The method is shown to require computational effort similar to local linearization, but does not require discrete computation of a functional Jacobian for solution. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...]

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