Multidimensional characteristic-based solid boundary condition for incompressible flow calculations

Using the artificial compressibility (AC) approach for incompressible flows, the Navier–Stokes equations are coupled together to obtain solutions for steady flows, where marching in time methods are applicable. In this study, we present a new method that employs the multidimensional characteristics of AC equations to calculate the solid boundary conditions. The first multidimensional characteristic-based scheme (MCB) for incompressible flows was proposed in a previous study. In the present study, this idea is implemented by using the characteristic structure of AC equations near solid walls together with a ghost cell method to satisfy the solid boundary conditions. We test the new proposed method with two well-known benchmark problems, where the results show that the accuracy and convergence speed of the MCB scheme is improved in many cases.