A common strategy for solving steady equations is to march the associated unsteady equations in time until the solution converges to a stationary result. In the case of the compressible Euler equations, this approach has the important advantage of transforming the problem from a mixed hyperbolic-elliptic problem in the steady state to a strictly hyperbolic problem in the transient stages. Unfortunately, this approach also introduces any stiffness due to the unsteady equations into the convergence process for the steady equations. For example, in a nearly incompressible flow, the speed of sound is significantly faster than the local flow speed.
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