Abstract
Abstract In this paper, we study a plane-parallel flow of the homogeneous inviscid incompressible fluid. The close attention is paid to the free boundary deformation under the forces of self-gravitation and fluid rotation. The problem is studied numerically, i.e., we propose the numerical algorithm for the free boundary calculation. The algorithm is based on the boundary element method. Algorithm applications include calculation of thin cumulative jets. The second point of interest is numerical results validation. The computational accuracy is controlled through the conservation laws. In this paper, we provide the derivation of conservation laws of energy and angular momentum for the case of rotating flows. In addition, we analytically investigate dynamics of two-dimensional near-equilibrium shapes and check the consistency of the analytical and numerical results.
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