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Modeling of nonparallel effects in temporal direct numerical simulations of compressible boundary-layer transition. (English) Zbl 0823.76033

One important alternative to spatial direct numerical simulation of a growing boundary-layer transition is a temporal direct numerical simulation (TDNS), where the flow is assumed to be locally parallel and the transition develops in time. To model nonparallel effects of a growing boundary layer, the TDNS allows the boundary layer to grow in time. For a compressible boundary layer, we first split the variation of the flow field in the streamwise direction into a slowly evolving part and a fast and small-scale fluctuation part. By Taylor-expanding the slowly evolving large-scale part, this study shows that the Navier-Stokes operator can be reformulated as a power series of the perturbation parameter \((x- x_ 0)\), yielding one set of equations for each power. Each set of these equations has a periodic solution in the streamwise direction, and therefore a modified TDNS method can be employed to solve these equations. Only the first set of the equations is considered in the applications presented.

MSC:

76E99 Hydrodynamic stability
76N20 Boundary-layer theory for compressible fluids and gas dynamics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M20 Finite difference methods applied to problems in fluid mechanics
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