A convergent finite element formulation for transonic flow

Berger, Harald

doi:10.1007/bf01396647

Cited by 18 publications

(16 citation statements)

References 20 publications

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“…The result of Theorem 5.5 is a generalization of the results proved in the papers by Berger in [6] and [5].…”

Section: This Impliessupporting

confidence: 53%

“…The purpose of this section is a convergence proof for the sequence {( u h , λ h , β h )} h>0 of solutions of problem (4.5). The main underlying ideas for this proof go back to Berger [6], who has proved the convergence of the interior problem with a simplified boundary condition on polygonal domains. An extension of this work to domains with arbitrary curved boundaries can be found in Berger and Feistauer [7].…”

Section: 2mentioning

confidence: 99%

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Analysis of a FEM/BEM coupling method for transonic flow computations

Berger¹,

Warnecke

Wendland

1997

Math. Comp.

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Abstract. A sensitive issue in numerical calculations for exterior flow problems, e.g. around airfoils, is the treatment of the far field boundary conditions on a computational domain which is bounded. In this paper we investigate this problem for two-dimensional transonic potential flows with subsonic far field flow around airfoil profiles. We take the artificial far field boundary in the subsonic flow region. In the far field we approximate the subsonic potential flow by the Prandtl-Glauert linearization. The latter leads via the Green representation theorem to a boundary integral equation on the far field boundary. This defines a nonlocal boundary condition for the interior ring domain. Our approach leads naturally to a coupled finite element/boundary element method for numerical calculations. It is compared with local boundary conditions. The error analysis for the method is given and we prove convergence provided the solution to the analytic transonic flow problem around the profile exists.

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“…The result of Theorem 5.5 is a generalization of the results proved in the papers by Berger in [6] and [5].…”

Section: This Impliessupporting

confidence: 53%

Section: 2mentioning

confidence: 99%

Analysis of a FEM/BEM coupling method for transonic flow computations

Berger¹,

Warnecke

Wendland

1997

Math. Comp.

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“…Therefore, the problem for transonic flow with a LSR in a curvilinear channel can be formulated in a rectangle of the plane (x, y) as follows. Find a solution ϕ(x, y) of equation (2) in the domain G = {(x, y) ∈ R 2 ; 0 < x < l, −1 < y < 1} endowed with the boundary conditions:…”

Section: Formulation Of the Problem Uniqueness Of The Solutionmentioning

confidence: 99%

Solvability of a problem for transonic flow with a local supersonic region

Kuzmin

2001

NoDEA, Nonlinear differ. equ. appl.

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A nonlinear perturbation problem for steady two-dimensional inviscid transonic flow with a local supersonic region is considered. A damping condition is prescribed on a portion of the boundary in order to prevent the arising of shock waves in the flow. The existence of a smooth solution to the problem is established. A proof is based on the Fredholm alternative and on a technique for uniqueness analysis worked out by and Cook (1978).2000 Mathematics Subject Classification: 35M10, 76H05.

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“…Then, one of the most common procedures consists of applying the boundary integral method (BIM) to the unbounded domain, and the finite element method (FEM) to the bounded one. This technique, called the coupling of BIM and FEM, has shown to be very effective to solve linear as well as nonlinear exterior boundary value problems with a linear homogeneous equation in the unbounded region (see, e.g., [1][2][3][4][5][6][7][8][9], [14], [16], [17], [21], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A boundary-field equation method for a nonlinear exterior elasticity problem in the plane

1996

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This paper presents a new method for solving a nonlinear exterior boundary value problem arising in two-dimensional elasto-plasticity. The procedure is based on the introduction of a sufficiently large circle that divides the exterior domain into a bounded region and an unbounded one. This allows us to consider the Dirichlet-Neumann mapping on the circle, which provides an expficit formula for the stress in terms of the displacement by using an appropriate infinite Fourier series. In this way we can reduce the original problem to an equivalent nonlinear boundary value problem on the bounded domain with a natural boundary condition on the circle. Hence, the resulting weak formulation includes boundary and field terms, which yields the so called boundary-field equation method. Next, we employ the finite Fourier series to obtain a sequence of approximating nonlinear problems from which the actual Galerkin schemes are derived. Finally, we apply some tools from monotone operators to prove existence, uniqueness and approximation results, including Cea type error estimates for the corresponding discrete solutions.

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A convergent finite element formulation for transonic flow

Cited by 18 publications

References 20 publications

Analysis of a FEM/BEM coupling method for transonic flow computations

Analysis of a FEM/BEM coupling method for transonic flow computations

Solvability of a problem for transonic flow with a local supersonic region

A boundary-field equation method for a nonlinear exterior elasticity problem in the plane

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