Abstract
The governing equations of steady supersonic or hypersonic viscous flow are the Navier–Stokes (NS) equations, which can be simplified for some simple cases by omitting the viscous derivatives in the streamwise direction. The earlier cross-plane solution will be a good initial guess for the current cross-plane computation if the distance is not large between the two. Therefore, the numerical solution of the parabolized Navier–Stokes (PNS) equations offers a good opportunity for using Newton's method for the initial guess. The benefits of using the structured grid are that it is easy for ordering the cells; it makes the Jacobian matrix of the implicit method structured; it is more suitable for the discretization of boundary layers; and in parallel calculation, it is easy to implement the domain decomposition technique. The test case produces a flow that has a large separated flow region with an embedded shock wave in the leeward side of the object and strong gradients in the thin boundary layer on the windward side.
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