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Extension of centered hydrodynamical schemes to unstructured deforming conical meshes: the case of circles. (English. French summary) Zbl 1330.76082
Summary: In a prior work [B. Boutin et al., ESAIM, Proc. 32, 31–55 (2011; Zbl 1235.76079)], a curvilinear bi-dimensional finite volume extension of Lagrangian centered schemes GLACE [G. Carré et al., J. Comput. Phys. 228, No. 14, 5160–5183 (2009; Zbl 1168.76029)] on unstructured cells, whose edges are parameterized by rational quadratic Bézier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme [P.-H. Maire et al., SIAM J. Sci. Comput. 29, No. 4, 1781–1824 (2007; Zbl 1251.76028)] to these cells. To simulate flows with evolving large deformations, we write a formalism allowing the time evolution of the conic parameter. As an example, this allows an edge changing from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a mesh whose edges are circle segments with non fixed centers. We show that this formalism extends also the previous work [A. Claisse et al., J. Comput. Phys. 231, No. 11, 4324–4354 (2012; Zbl 1426.76350)] (which is equivalent to [Boutin, loc. cit.] when conic edges are all circles). This is a necessary first step toward general conical deformation.
MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76Bxx Incompressible inviscid fluids
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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