Virtual boundary method for inviscid transonic flow over supercritical airfoils

A direct virtual boundary method is presented for flow modeling over complex geometries. The main characteristic of the method is that the internal boundary condition at the surface of the embedded body is generated using a function that determinate the suitable body force that ensures the no slip condition directly from the momentum equation. The body force is spread from the Lagrangian to the Eulerian mesh using a Dirac delta function combined with a smooth distribution function. The solver is based on the finite difference approach; integration is carried out with a predictor corrector method, which has second order of precision in both space and time. The flow model is based on the equations of Euler for inviscid compressible flow in two dimensions. The method is employed to simulate the flow at transonic regime over the supercritical airfoils RAE 2822 and NLR 7301. Results show good agreement between numerical and experimental data.