PNS algorithm for solving supersonic flows with upstream influences

Abstract

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Correlations to predict turbulent streamwise influence regions and onset of transition in supersonic flows

“…The TIPNS algorithm has been demonstrated by Miller et al [40,43] to be accurate over the range of flow conditions that are considered in the present study. The accuracy of the turbulent relaxation model in computing turbulent flows was demonstrated in Ref.…”

“…Modifications to the PNS equations to enable capturing the upstream influence effects lead to the IPNS algorithm developed by Miller et al [43,46]. The IPNS algorithm has the capacity to accurately compute attached or separated supersonic viscous flows with upstream influence.…”

“…In addition, the newly developed correlations could be coupled with those developed previously for both laminar [43] and turbulent flow [17,18] in order to automate the computation of various flowfields.…”

A new forward-backward sweeping parabolized Navier-Stokes algorithm with application to magnetohydrodynamic flows

“…Recently, a new numerical approach has been developed [1][2][3][4][5] that iteratively solves the parabolized Navier-Stokes (PNS) equations. In this approach, the standard single-sweep PNS method is used to march the solution in the streamwise direction in re gions where there are negligible upstream influences.…”

“…The IPNS (iterative PNS) algorithm [1][2][3] splits the streamwise flux vector using the Vigneron splitting [6] and can be applied to flows with moderate upstream influences and small streamwise separated regions. The TIPNS (time iterative PNS) algorithm [4,5] splits the streamwise flux vector using the Steger-Warming splitting [7] and may retain the time derivative terms.…”