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**Parallel fluid dynamics computations in aerospace applications.**
*(English)*
Zbl 0862.76033

Summary: Massively parallel finite element computations of the compressible Euler and Navier-Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables, and the streamline-upwind/Petrov-Galerkin stabilization method is used to prevent potential numerical oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods, and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large-scale three-dimensional problems are solved using a matrix-free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in three-dimensional and those involving moving boundaries interactig with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation, and the ones involving moving boundaries are solved using the deformable-spatial-domain/stabilized-space-time formulation.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

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

65Y05 | Parallel numerical computation |

### Keywords:

Euler equations; Navier-Stokes equations; streamline-upwind/Petrov-Galerkin stabilization method; matrix-free iteration technique; moving boundaries; boundary layers; shocks; semidiscrete formulation; deformable-spatial-domain/stabilized-space-time formulation
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\textit{S. K. Aliabadi} and \textit{T. E. Tezduyar}, Int. J. Numer. Methods Fluids 21, No. 10, 783--805 (1995; Zbl 0862.76033)

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