A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations

The interaction of an oblique shock with a laminar boundary layer on an adiabatic flat plate is analysed by solving the Navier-Stokes equations numerically. Mach numbers range from 1.4 to 3.4 and Reynolds numbers range from 105 to 6 × 105. The numerical results agree well with experiments. The pressure distribution at the edge of the boundary layer is proposed as a sensitive indicator of the numerical resolution. Local and global properties of the interaction region are discussed. In the vicinity of the separation point, local scaling laws of the free interaction are confirmed. For the length of the separation bubble a new similarity law reveals a linear influence of the shock strength. A comparison with the triple-deck theory shows that, for finite Reynolds numbers, the triple deck tends to overestimate the lengthscale substantially and that this discrepancy increases with increasing Mach number. The triple-deck model of displacing the main part of the boundary layer is substantiated by the numerical results. An asymmetrical structure within the separation bubble causes a characteristic distribution of the wall shear stress.

On the lengthscales of laminar shock/boundary-layer interaction

On presente differentes techniques d'adaptation pour le calcul des ecoulements visqueux laminaires bidimensionnels. Application a des ecoulements subsoniques et supersoniques

Adaptation methods for a new Navier-Stokes algorithm

A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.

A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity

Non-Navier Stokes viscous flow computations☆

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

/pdf/numerical-solutions-of-the-navier-stokes-equations-for-the-vvj6onlvet.pdf

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

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Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner