Time-Marching Finite-Difference Schemes for Three-Dimensional Compressible Euler Equations

Abstract

Explicit and implicit time-marching finite-difference schemes are proposed for analysing three -dimensional steady and unsteady inviscid transonic flows. These schemes are different from the existing methods since the Euler equations of contravariant velocities in general curvilinear coordinates are used. However, some computational techniques used in the existing methods, such as linearization, diagonalization and upstreaming are also applied to these schemes. The finally obtained equations for the numerical computation have almost the same complexity as the corresponding existing methods. The remarkable feature of these methods is the ability to treat solid wall boundary conditions easily and exactly including, implicit schemes. A calculated result of shocked transonic flow through a converging-diverging square nozzle is shown.