Numerical solutions of the supersonic, laminar flow over a two-dimensional compression corner

Carter, James E.

doi:10.1007/bfb0112678

Cited by 36 publications

(66 citation statements)

References 4 publications

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“…Generally, a good agreement is observed except for the peak values at the stagnation point, as mentioned before. The location of the separation point happens at x = 0.89 showing an appropriate compatibility with the results presented in the [5,21,45] ranging from x = 0.84 to x = 0.89. …”

Section: Example Iv: Compression Cornersupporting

confidence: 81%

“…The results demonstrate the good behavior of the presented formulation in capturing the shock wave and the boundary layer. The obtained density value and the y component of the velocity along the line x = 1.2 are compared in Figures 13a and 13b, respectively, with the results presented in [5]. Although the obtained peak point values of both the density and y component of the velocity are not coincident with the reference ones, an overall good agreement with the reference results can be observed.…”

Section: Example Ii: Subsonic Viscous Flow Past a Naca0012 Airfoilsupporting

confidence: 52%

“…The obtained C p and C f distributions along the plate surface are compared to the ones presented by Carter [5] in Figure 17 and Figure 18, respectively. Generally, a good agreement is observed except for the peak values at the stagnation point, as mentioned before.…”

Section: Example Iv: Compression Cornermentioning

confidence: 93%

“…The problem data is extracted from [5] where the flow for Re = 16800, M ∞ = 3.0 and α = 0 • enters the domain passing over a flat plate and then over a compression corner of 10 • inducing the shock wave and the boundary layer initiated from the leading edge of the plate. The Reynolds number is calculated using the free stream values and the distance between the leading edge of the plate and the compression corner.…”

Section: Example Iv: Compression Cornermentioning

confidence: 99%

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An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

Kouhi

Oñate

2015

Comput Mech

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A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors [24]. In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.

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Section: Example Iv: Compression Cornersupporting

confidence: 81%

Section: Example Ii: Subsonic Viscous Flow Past a Naca0012 Airfoilsupporting

confidence: 52%

Section: Example Iv: Compression Cornermentioning

confidence: 93%

Section: Example Iv: Compression Cornermentioning

confidence: 99%

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An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

Kouhi

Oñate

2015

Comput Mech

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“…The second problem, called the Carter problem, 32 consists of a viscous¯ow over an in®nitely thin at plate at zero angle of attack in the supersonic regime (M 3), with a Reynolds number of 1000 based on the freestream values and the distance from the leading edge of the plate. In this case we show the behaviour of the code in problems where a strong curved shock interacts with a boundary layer starting at the leading edge of the plate.…”

Section: Flow Over A¯at Platementioning

confidence: 99%