Introduction of oblique plane waves through a forcing source term in Euler equations

The propagation of shock waves generated by a transonic flow at the tip of a propeller blade is numerically calculated in order to determine the pressure footprint on an aircraft fuselage. An academic case is first proposed to validate the methodology. An incoming signal is built up as oblique harmonic plane waves. The signal is introduced in the computational domain using a Gaussian volume forcing term in the conservation of mass and energy equations. The Euler equations are solved in two dimensions using finite-difference schemes with low dispersion and dissipation. Selective filtering has also been integrated in the algorithm to remove grid-to-grid oscillations. The numerical solution is compared to an analytical solution based on the tailored Green function. An illustration for a realistic open rotor is then considered. The pressure signal near the blade tip, determined from a preliminary RANS simulation, is introduced using a volume source in a solver of the Euler equations.