EBR schemes with curvilinear reconstructions of variables in the near-wall region

Higher accuracy vertex-centered EBR schemes for gasdynamic simulations on unstructured meshes are developed. The schemes are equipped with the option of using a quasi-one-dimensional curvilinear stencil for reconstructing variables on a structured or semi-structured anisotropic mesh in the near-wall region. In the two-dimensional case, the use of curvilinear reconstruction leads to the natural transformation of an EBR scheme into a structured mesh finite-volume method. In the three-dimensional case, an original algorithm for finding stencil points and corresponding metric coefficients is developed to implement curvilinear reconstructions of variables in prismatic layers. The effect exerted by curvilinear reconstructions used in EBR schemes as applied to external flow problems is demonstrated on the well-known test problem of the flow around the NACA0012 airfoil considered in two- and three-dimensional formulations. The new algorithm is validated by comparing the solution with experimental data and numerical results of other authors. The use of curvilinear reconstructions in EBR schemes enhances the stability of the method and improves the accuracy of the numerical results.