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 gri d approach is developed for solving the 2D steady state Euler equation s describing supersonic gas flows without streamwise separation. A gri d adapted to the solution is generated by using a variational method o ptimizing such important properties of a grid as smoothness, orthogona lity, and grid cell volume variation simultaneously. The weight functi on in the integral of adaptation is constructed, so that the grid line s are accumulated near strong gradients and curvatures of the solution curve. A special treatment of the boundary points is proposed to dete rmine the location of nodes near slope discontinuities of the boundary mesh line. The noniterative implicit space-marching method of Y. C. V igneron ct al. is applied to solve the Euler equations written in an a rbitrary curvilinear system of coordinates. The streamwise and transve rse derivatives in the governing equations are approximated by the sec ond-order upwind Richardson and second-order symmetric TVD schemes, re spectively. Implicit boundary condition procedure based on the theory of characteristics for hyperbolic systems of equations is employed. Nu merical calculations show that the resolution of strong gradient now f ields can significantly be improved by using the grid adapted to the s olution the number of grid nodes is the same. (C) 1998 Academic Press.