EBR schemes with curvilinear reconstructions for solving two-dimensional external flow problems

This paper is devoted to the development of vertex-centered EBR schemes for numerical simulation of aerodynamics problems. We propose to equip these schemes with the curvilinear reconstructions in the boundary layer region. In the considered two-dimensional case, the curvilinear reconstructions provide the natural transformation of EBR scheme into a structured finite-volume method. The advantage of this approach for numerical simulations of external flows is shown. As a test case, two-dimensional stationary flow around the NACA0012 profile is considered. Validation of the new algorithm is carried out by comparison with the known experimental data and the numerical results obtained by other authors. The involvement of curvilinear reconstructions improves the algorithm stability and accuracy.