| A study of various approximate Jacobians in conjunction with relaxation schemes for a numerical solution of the Euler equations is undertaken. A finite-volume formulation of the Euler equations is developed using Roe's approximate Riemann solver as the numerical flux function. Three different approximate Jacobians based on the Jacobian Spectral Radius, Flux Vector Splitting, and Flux Difference Splitting are examined. Their effects on Point Jacobi, Lower-Upper Symmetric Gauss-Seidel, Vertical Line Jacobi and Vertical Line Symmetric Gauss-Seidel are studied. Solutions are computed for subsonic and transonic flows about a circular arc airfoil in a channel, and flow past a supersonic ramp. It is concluded that the Lower-Upper Symmetric Gauss-Seidel relaxation scheme along with the Flux Vector Splitting-based approximate Jacobian produces rapid convergence for all flow regimes considered. |
