A numerical method for compressible viscous fluid flows.

摘要

The steady two-dimensional compressible Navier-Stokes equations are solved using an iterative pseudo-time relaxation technique. An implicit first-order accurate Euler scheme is implemented after augmenting the steady governing equations by pseudo-time derivative terms, including artificial compressibility in the continuity equation and preconditioning in the energy equation. These augmented equations are modified by lagging certain flow variables in pseudo-time and by applying approximate factorization and an alternating direction implicit (ADI) method to split the solution procedure into two successive sweeps.; Spatial discretization is performed on a stretched staggered grid using central differencing. Then, the momentum equations are decoupled with the elimination of the pressure terms using the continuity equation. The problem is thus reduced to the solution of a series of scalar tridiagonal systems of equations.; The computational method is validated for laminar incompressible flows in channels with downstream-facing steps and for laminar compressible flows past symmetric airfoils.