Space-marching method for calculating steady supersonic flows on a grid adapted to the solution

A noniterative implicit space-marching method based on an adaptive grid approach is developed for solving the 2D steady state Euler equations describing supersonic gas flows without streamwise separation. A grid adapted to the solution is generated by using a variational method optimizing such important properties of a grid as smoothness, orthogonality, and grid cell volume variation simultaneously. The weight function in the integral of adaptation is constructed, so that the grid lines are accumulated near strong gradients and curvatures of the solution curve. A special treatment of the boundary points is proposed to determine the location of nodes near slope discontinuities of the boundary mesh line. The noniterative implicit space-marching method of Y. C. Vigneron ct al. is applied to solve the Euler equations written in an arbitrary curvilinear system of coordinates. The streamwise and transverse derivatives in the governing equations are approximated by the second-order upwind Richardson and second-order symmetric TVD schemes, respectively. Implicit boundary condition procedure based on the theory of characteristics for hyperbolic systems of equations is employed. Numerical calculations show that the resolution of strong gradient now fields can significantly be improved by using the grid adapted to the solution the number of grid nodes is the same. (C) 1998 Academic Press.