On numerical investigation of transonic turbulent flows near a wing by implicit higher-order schemes (Q2729349)

The article is devoted to numerical simulation of transonic turbulent flows near a wing. It is well known that, by the investigation of transonic flows, the modeling of a thin boundary layer makes explicit schemes ineffective. The aim of the article is to demonstrate that implicit schemes of higher-order accuracy present an effective tool for numerical simulation. Three high-accuracy implicit finite difference schemes are exposed: a third-order Runge-Kutta scheme, a second-order Runge-Kutta scheme which is fifth-order accurate for stationary solutions, and a scheme which is first-order accurate with respect to time and third-order accurate for spatial variables. The schemes are constructed using the following principles: conservation property, preserving monotonicity of solutions, and guaranteeing the entropy dissipation. Numerical tests demonstrate sufficient accuracy of calculations.