An efficient upwind relaxation–sweeping algorithm for three-dimensional euler equations

An efficient finite—volume algorithm for three—dimensional Euler equations is presented. The spacial discretization is based on Van Leer's flux vector splitting. The flow field is analyzed by alternating sweeping in the spanwise direction and local Gauss-Seidel iteration on each vertical streamwise plane. Very large time step can be obtained since no factorization error is introduced and it leads to very rapid convergence rate. The memory resources are greatly saved since the Jacobians, the residual R and the δUⁿ⁺¹ are stored only in one iterating plane. Two internal transonic flows are calculated to show the efficiency and accuracy.