УЧЁТ ПОДКРЕПЛЕНИЙ ПРИ РАСЧЁТЕ ОБОЛОЧЕК ВАРИЦИОННО-РАЗНОСТНЫМ МЕТОДОМ

A ribbed shell of a general form consisting from a skin, a position of points of the middle surface of which is determined by the orthogonal curvilinear coordinates ?, ?, and curved ribs, lying along coordinate linesareconsidered. At the moment, a classical approach is taken in the work to model ribs by the rod theory of Kirchhoff-Clebsch. A shell is described by the theory of thin shells of the Kirchhoff-Love.Рассматривается ребристая оболочка общего вида, состоящая из обшивки, положение точек срединной поверхности которой определяется криволинейными ортогональными координатами ?, ?, и криволинейных рёбер, расположенных вдоль координатных линий.В данный момент в работе принят ставший уже классическим подход моделирования рёбер теорией стержней Кирхгофа-Клебша. Оболочка описывается теорией тонкостенных оболочек Кирхгофа-Лява

On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations

Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms that are specific to meshfree methods have often been overlooked. In this paper, we study the drawbacks of conventionally used meshfree Generalized Finite Difference Method~(GFDM) schemes for Lagrangian incompressible Navier-Stokes equations, both operator splitting schemes and monolithic schemes. The major drawback of most of these schemes is inaccurate local approximations to the mass conservation condition. Further, we propose a new modification of a commonly used monolithic scheme that overcomes these problems and shows a better approximation for the velocity divergence condition. We then perform a numerical comparison which shows the new monolithic scheme to be more accurate than existing schemes