On the Cabaret Scheme for Incompressible Fluid Flow Problems with a Free Surface

Abstract

This paper proposes a new approach for solving problems of vortex structures’ interaction with a free surface. The second-order accuracy finite-difference scheme based on the well-known CABARET scheme is suggested for incompressible viscous fluid with a free surface. The CABARET method in the case of an incompressible medium additionally solves the problem of the velocity field’s solenoidation. Solving such a problem implies solving a system of linear equations with respect to the pressure variable and then taking the pressure gradient into account when calculating equations of motion. Solving the system of linear equations is a separate related problem that is not included in the description of the CABARET method, and this paper presents only the problem statement without specifying a specific method for solving the system.