Méthode de couplage conservative entre un fluide compressible non-visqueux et une structure tridimensionnelle déformable pouvant se fragmenter

摘要

We develop a coupling method between an inviscid compressible fluid and a three dimensional mobile structure. We consider first a rigid structure, then a deformable, and finally a fragmenting one. The coupling hinges on a Conservative Immersed Boundary method combined with a Finite Volume method for the fluid and a Discrete Element method for the structure. The method yields conservation of mass, momentum, and energy of the system. The method also exhibits consistency properties, such as the absence of numerical roughness on a rigid wall. The method is explicit in time in the case of a rigid structure, and semi-implicit when the structure is deformable. The time semi-implicit method avoids that tangential deformations of the structure impact the fluid, and the method converges geometrically with a non-restrictive CFL condition on the time step. We present numerical results showing the robustness of the method in the case of a rigid sphere lifted by a shock wave, a clamped beam flexed by a shock wave, and a cylinder undergoing fragmentation owing to an intern explosion