Конференции ИВТ СО РАН

MIT-2009
Международная конференция "Математические и информационные технологии"
(VIII конференция "Вычислительные и информационные технологии в науке, технике и образовании")

Копаоник, Сербия, 27 - 31 августа 2009 года;
Будва, Черногория, 31 августа - 5 сентября 2009 года

Тезисы докладов

A truly third order finite volume schene on quadrilateral mesh

Petkovic D., Petrovic M.

Prirodno - matematicki Fakultet,
Kosovska Mitrovica ()

A third order finite volume method on a quadrilateral mesh is presented. By using quadrangles instead of rectangles as a basic element of the mesh, full generalization is archived. This work holds on a simple but valuable conservative rule: inside a certain special domain (volume) the total amount of a contained quantity (such as mass, energy, momentum) is preserved. Said in another way, the total quantity in the volume doesn’t change except by flow (or due to the fluxes) across the boundary of a domain. Efficient tools for solving the conservation laws are the finite volume methods. These methods are dealing with volumes (cells) and with averaged quantities within. In each of these cells we have exact conservation. The dynamics of the average is determined by point values of the flux along the boundary. The aim is to obtain a third order accurate numerical solution. This gives a motivation for the reconstruction of the numerical flux by some known functions (polynomial, hyperbolic, logarithmic). In this work local double logarithmic reconstruction was used. The components needed for developing LDRD functions are second order approximation to the first derivatives. These approximations are actually a crucial problem in this thesis and were solved specifically according to multidimensional numerical integration theory.

Примечание. Тезисы докладов публикуются в авторской редакции

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