Abstract
We study an initial–boundary value problem with free boundary for one-dimensional equations of viscous gas dynamics. The problem models the motion of a crankshaft mechanism under gas pressure. It is assumed that the gas fills a cylinder, which is modeled by the interval \([0,1]\). A variable point \(a(t)\in[0,1]\) models a piston moving inside the cylinder. The piston is assumed to be connected to a planar three-link crankshaft mechanism. We also assume that a velocity distribution on the boundary of the cylinder and a density distribution on gas inflow segments are given. The gas motion is described by the one-dimensional Navier–Stokes equations of viscous compressible fluid dynamics. It is required to determine the joint motion of the gas and crankshaft mechanism. We prove that this problem has a weak renormalized solution.
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Plotnikov, P.I., Sokołowski, J. Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas. Proc. Steklov Inst. Math. 310, 220–249 (2020). https://doi.org/10.1134/S0081543820050181
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DOI: https://doi.org/10.1134/S0081543820050181