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On the numerical solution of sparse linear systems emerging in finite volume discretizations of 2D Boussinesq-type models on unstructured grids

Delis Anargyros, Kazolea Maria, Gaitani Maria

Απλή Εγγραφή


URIhttp://purl.tuc.gr/dl/dias/64E73AE7-D00C-4A94-B9E9-951B0BB76CB1-
Αναγνωριστικόhttps://doi.org/10.3390/w14213584-
Αναγνωριστικόhttps://www.mdpi.com/2073-4441/14/21/3584-
Γλώσσαen-
Μέγεθος21 pagesen
ΤίτλοςOn the numerical solution of sparse linear systems emerging in finite volume discretizations of 2D Boussinesq-type models on unstructured gridsen
ΔημιουργόςDelis Anargyrosen
ΔημιουργόςΔελης Αναργυροςel
ΔημιουργόςKazolea Mariaen
ΔημιουργόςΚαζολεα Μαριαel
ΔημιουργόςGaitani Mariaen
ΔημιουργόςΓαϊτανη Μαριαel
ΕκδότηςMDPIen
ΠερίληψηThis work aims to supplement the realization and validation of a higher-order well-balanced unstructured finite volume (FV) scheme, that has been relatively recently presented, for numerically simulating weakly non-linear weakly dispersive water waves over varying bathymetries. We investigate and develop solution strategies for the sparse linear system that appears during this FV discretisation of a set of extended Boussinesq-type equations on unstructured meshes. The resultant linear system of equations must be solved at each discrete time step as to recover the actual velocity field of the flow and advance in time. The system’s coefficient matrix is sparse, un-symmetric and often ill-conditioned. Its characteristics are affected by physical quantities of the problem to be solved, such as the undisturbed water depth and the mesh topology. To this end, we investigate the application of different well-known iterative techniques, with and without the usage of preconditioners and reordering, for the solution of this sparse linear system. The iiterative methods considered are the GMRES and the BiCGSTAB, three preconditioning techniques, including different ILU factorizations and two different reordering techniques are implemented and discussed. An optimal strategy, in terms of computational efficiency and robustness, is finally proposed which combines the use of the BiCGSTAB method with the ILUT preconditioner and the Reverse Cuthill–McKee reordering.en
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2023-09-07-
Ημερομηνία Δημοσίευσης2022-
Θεματική ΚατηγορίαBoussinesq-type equationsen
Θεματική ΚατηγορίαFinite volumesen
Θεματική ΚατηγορίαUnstructured meshesen
Θεματική ΚατηγορίαSparse matricesen
Θεματική ΚατηγορίαPreconditioningen
Θεματική ΚατηγορίαReorderingen
Βιβλιογραφική ΑναφοράA. I. Delis, M. Kazolea, and M. Gaitani, “On the numerical solution of sparse linear systems emerging in finite volume discretizations of 2D Boussinesq-type models on unstructured grids,” Water, vol. 14, no. 21, Nov. 2022, doi: 10.3390/w14213584.en

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