Treatment of Nonmatched Grids for High-Accuracy Navier-Stokes Solutions

This paper handles the problem of accuracy loss for flow solutions on computational domains with a heterogeneous discretization on the subdomains. The problem occurs, e.g., when a composite multiblock mesh comprises blocks with different grid resolutions on the common boundary face. The problem is especially troublesome for high-accuracy solutions, in which tailoring of heterogeneous meshes frequently brings the loss of accuracy on a global scale. This paper focuses on the treatment of non-point-to-point structured multiblock grids, in which face-matched block boundaries are not necessarily point-matched. In the context of high-accuracy characteristic finite volume schemes for three-dimensional Navier―Stokes equations, a new approach is proposed that handles composite grids without the need in geometrical adjustment of boundary cells or any other grid-related preprocessing. In the proposed approach, interblock cell clusters are formed that contain boundary cells from the neighboring blocks of different resolutions. For each such cluster, the residuals of the Navier―Stokes equations are computed and then distributed among the cells of the host cluster by directly minimizing the flux imbalance in an appropriate norm. Outside these clusters, the residuals are computed in the regular way. The method allows automatic preservation of the conservative property of fluxes by placing constraints upon the optimum, it does not change the stability properties of the basic high-accuracy scheme and ensures a sufficiently high level of approximation on grids with reduced resolution. The results that include a number of numerical tests for two- and three-dimensional wings indicate good accuracy and robustness of the method and its applicability to full-scale Navier―Stokes computations.