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Implementation of boundary conditions for meshless methods. (English) Zbl 0963.76068
Summary: Boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmound many initial difficulties due to the lack of a finite-element-like Kronecker delta condition. Furthermore, it is frequently desirable, especially in fluid mechanics, to impose general, nonlinear boundary and interface constraints. This paper describes an algorithm based on d’Alembert’s principle that can be used for general constraints both in meshless methods and finite elements. First, we develop a method of partitioning meshless shape functions suitable for imposing linear boundary conditions. Subsequently, an analogous method is developed for nonlinear constraints. Special attention is given to imposing general boundary and fluid-structure interface conditions on the Navier-Stokes equations in terms of conservative variables. We present numerical results which are obtained by using d’Alembert’s principle with the reproducing kernel particle method, for viscous supersonic flow past NACA 1712 airfoil.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics, general
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