Stability investigation of Runge–Kutta schemes with artificial dissipator on curvilinear grids for the Euler equations Original Research Article

By using the Fourier method we study the stability of a three-stage finite volume Runge–Kutta time stepping scheme approximating the 2D Euler equations on curvilinear grids. By combining the analytic and numeric stability investigation results we obtain an analytic formula for stability condition. The results of numerical solution of a number of internal and external fluid dynamics problems are presented, which confirm the correctness of the obtained stability condition. It is shown that the incorporation of the artificial dissipation terms into the Runge–Kutta scheme does not impose additional restrictions on time step in cases of smooth flows or flows with weak shocks. In cases of strong shocks, the use of artificial viscosity leads to the reduction of the maximum time step allowed by stability in comparison with the case of the absence of artificial viscosity.