Assessment of Characteristic Boundary Conditions Based on the Artificial Compressibility Method in Generalized Curvilinear Coordinates for Solution of the Euler Equations

Abstract

Abstract The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary conditions. Two benchmark test cases are computed to investigate the accuracy and performance of the characteristic boundary conditions implemented compared to the simplified boundary conditions. The sensitivity of the solution obtained by applying the characteristic boundary conditions to the different numerical parameters is also studied. Indications are that the characteristic boundary conditions applied improve the accuracy and the convergence rate of the solution compared to the simplified boundary conditions.