Monolithic balance-characteristic method for solving problems of interaction of liquid and gas with deformable objects

A new conservative-characteristic method for solving problems of interaction of liquid and gas flows with deformable objects is built. The proposed method is a representative of the family of so-called monolithic (or seamless) methods, in which both the gas and the deformation of objects are calculated using a single numerical scheme that allows to naturally model the interface between gas and bodies. The resulting method is explicit, easily scalable, and uses Lagrangian coordinates to model deformation of bodies and mixed Euler-Lagrangian coordinates to model gas flow. A key feature of the method is a time-reversible algorithm for moving the computational grid, which allows to exclude the numerical dissipation of the scheme. The method is tested on a number of onedimensional and two-dimensional problems: the transition of acoustic vibrations from a gas to an elastic medium, an air impact on an elastic body, generation of spherical acoustic waves by an oscillating beam.