A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries (Communications in Computational Physics, 2018)
In this paper, we describe how to construct a finite-difference shock-capturingmethod for the numerical solution of the Euler equation of gas dynamics onarbitrary two-dimensional domain Ω, possibly with moving boundary. The boundariesof the domain are assumed to be changing due to the movement of solid objects/obstacles/walls.Although the motion of the boundary could be coupled withthe fluid, all of the numerical tests are performed assuming that such a motion is prescribedand independent of the fluid flow. The method is based on discretizing theequation on a regular Cartesian grid in a rectangular domain ΩR ⊃ Ω. We identifyinner and ghost points. The inner points are the grid points located inside Ω, whilethe ghost points are the grid points that are outside Ω but have at least one neighborinside Ω. The evolution equations for inner points data are obtained from the discretizationof the governing equation, while the data at the ghost points are obtainedby a suitable extrapolation of the primitive variables (density, velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for bothfixed and time dependent domains. Several numerical experiments are conducted toillustrate the validity of the method. We demonstrate that the second order of accuracyis numerically assessed on genuinely two-dimensional problems.
Keywords: Compressible fluids; Euler equations of gas dynamics; ghost-cell extrapolation; moving boundaries; finite-difference shock-capturing methods.