Constrained least-squares reconstruction method for mixed grids

In order to enforce the effect of boundary conditions on the solution reconstruction of computational fluid dynamics (CFD) simulation, a constrained least-squares method based on arbitrary polyhedral mixed grids is investigated. To make the method simpler, a uniform constrained system is constructed through treating different boundary conditions in the same way. To make use of the advantages of both the elimination approach and the weighting approach, a mixed method is provided to solve the constrained system. The numerical experiments based on laminar plates show that setting the weighting coefficient to 5 is large enough in the weighting approach. The numerical results of a subsonic laminar flow over a plate and a transonic turbulent flow over ONERA-M6 demonstrate that the constrained least-squares method is more accurate than the original least-squares method, especially when bad quality grids are used near the boundary, and that the mixed method shows improved results as compared with the weighting approach.