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**On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods. II: Application to transonic flow simulations.**
*(English)*
Zbl 0555.76046

[For part I, see the first authors, ibid. 17/18, 619-657 (1979; Zbl 0423.76047).] - The main goal of this paper is to show how the general methods discussed in the first part apply to the solution of a class of rather complicated nonlinear problems of industrial interest, namely the numerical simulation of potential transonic flows for compressible inviscid fluids, in two and three dimensions. We recall in section 2 the governing equations and the various conditions that physical solutions have to verify, such as entropy and Kutta-Joukowsky conditions. We shall comment also on the possible existence of multiple physical solutions. In section 3, we recall the least squares formulation for the continuous problem discussed in the first part, and describe in section 4 the finite element approximation of the several above formulations of the continuous problem. In section 5, we discuss the finite element implementation of the entropy condition by upwinding of the density in the flow direction. In section 6 various numerical experiments illustrate the possibility of the above methods.

### MSC:

76H05 | Transonic flows |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

76M99 | Basic methods in fluid mechanics |

76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |

### Keywords:

variational formulation; lifting flow; conjugate gradient solution; numerical simulation of potential transonic flows for compressible inviscid fluids; entropy Kutta-Joukowsky conditions; existence of multiple physical solutions; least squares formulation; finite element approximation; numerical experiments### Citations:

Zbl 0423.76047### Software:

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\textit{M. O. Bristeau} et al., Comput. Methods Appl. Mech. Eng. 51, 363--394 (1985; Zbl 0555.76046)

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### References:

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