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تسجيل مستخدم جديدNon Conservative Products in Fluid Dynamics
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Fluid flow in pipes with discontinuous cross section or with kinks is described through balance laws with a non conservative product in the source. At jump discontinuities in the pipes geometry, the physics of the problem suggests how to single out a solution. On this basis, we present a definition of solution for a general BV geometry and prove an existence result, consistent with a limiting procedure from piecewise constant geometries. In the case of a smoothly curved pipe we thus justify the appearance of the curvature in the source term of the linear momentum equation. These results are obtained as consequences of a general existence result devoted to abstract balance laws with non conservative source terms.
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