A high-order finite-difference scheme to model the fluid-structure interaction in pneumatic seismic sources

Highlights: • The fluid-structure interaction inside a pneumatic seismic source is modeled by the nonlinear 1D Euler equations. • A provably stable numerical scheme modeling the fluid-structure interaction is derived. • Convergence studies confirm the accuracy of the scheme. The obtained convergence rates agree with theoretical results. • Simulation results captures many of the main features of the experimental data from a pneumatic seismic source. A high-order accurate finite-difference scheme modeling the fluid-structure interaction inside a pneumatic seismic source is presented. The model consists of two deforming fluid compartments separated by a moving shuttle. The fluid is governed by the 1D Euler equations. Well-posedness of the continuous problem is analyzed and proven in the frozen coefficient case. A stable discretization is derived using summation-by-parts operators with the boundary conditions imposed weakly using the simultaneous-approximation-term method. The theoretical convergence rate of the numerical scheme is verified by numerical experiments. Simulation results are compared to pressure measurements from inside a pneumatic seismic source and capture many of the features observed in the data.