Journal of Engineering Mathematics 27: 293-307, 1993. 293 ( 1993 Kluwer Academic Publishers. Printed in the Netherlands. Numerical aspects of a block structured compressible flow solver B.J. GEURTS* and H. KUERTEN Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands (*author for correspondence) Received 28 April 1992; accepted in revised form 20 January 1993 Abstract. A block structured compressible flow solver based on a finite volume approach with central spatial differencing is described and its performance in 2D on flow around an airfoil is studied. Variations in the number and dimensions of the blocks do not influence the convergence behavior nor the solution, irrespective of the relative positions of a possible shock and the block-interfaces. Mixed calculations, in which the governing equations, either Euler or Reynolds averaged Navier-Stokes, differ per block, give accurate results provided the Euler blocks are defined outside the boundary layer and or in the far field wake region. Likewise, extensive grid distortions near block interfaces can be allowed for outside the boundary layer. Finally, an unbalanced advancement in time, in which each block is advanced independently over several time steps gives no serious decrease in convergence rate. 1. Introduction The Reynolds averaged Navier-Stokes equations form a suitable basis for simulations of complex flow fields in which viscous effects play an important role, such as occur e.g. in transonic compressible flow around an airfoil. Accurate predictions of quantities of aeronautical interest (e.g. drag- and lift coefficients) predominantly require the use of structured grids. In order to treat more complex geometries such as a multi-element airfoil, it is therefore natural to concentrate on a block structured flow solver. This allows for a total grid composed of several blocks, each of which is represented by a structured grid and appropriate boundary conditions. In this way flow problems of increased complexity can be envisaged. The construction and performance of such a block structured flow solver are described in this paper. At present, only block structured grids in which the grid lines are continuous over block boundaries are considered. It will be shown that the introduction of such a block structure on the grid does not seriously influence the convergence behavior when compared to a situation without a block structure. This remains true even if the position of a shock coincides with a block interface. Moreover, mixed calculations in which the Navier-Stokes equations are defined in the boundary layer and the Euler equations outside this region yield accurate simulation results. However, in such cases the simulation results depend sensitively on the exact position of the 'Euler-Navier-Stokes' interface. The mixed calculation results differ considerably from the Navier-Stokes results even if the Euler blocks have their interface with Navier-Stokes blocks just inside the boundary layer. On the other hand the simulation results fully agree, for any definition of the Euler blocks outside the boundary layer. Extensive, local grid distortions near block interfaces do not seriously influence the results provided these distortions are small inside the boundary layer. Finally, the blocks can be advanced in time independently over several time steps without causing the rate of convergence to decrease significantly and giving an accurate prediction of aerodynamic properties (relative errors smaller than 1 percent). A significant amount of calculation time can hence be saved through the inclusion of Euler blocks outside the