Circular map for supercavitating flow in a multiply connected domain

A nonlinear free boundary-value problem of supercavitating flow past n + 1 hydrofoils is analyzed. To describe the cavities’ closure mechanism, the Tulin–Terent'ev single-spiral-vortex model is employed. The flow domain is considered as the image of an (n + 1)-connected circular domain. The conformal map is constructed in terms of the solutions to two Riemann–Hilbert problems of the theory of symmetric automorphic functions. One of the problems is homogeneous and its coefficients are continuous functions while the second problem is inhomogeneous and has discontinuous coefficients. The exact solutions to the problems are found by using quasiautomorphic and quasimultiplicative analogs of the Cauchy kernel. The case of a single plate is considered in detail and the numerical results are reported.