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Brooks, A.N. and Hughes, T.J.R. (1982) Streamline Upwind Petrov-Galerkin Formulation for Convection-Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations. Computer Methods in Applied Mechanics and Engineering, 32, 199-259.
https://doi.org/10.1016/0045-7825(82)90071-8

has been cited by the following article:

• TITLE: Application of the Hierarchical Functions Expansion Method for the Solution of the Two Dimensional Navier-Stokes Equations for Compressible Fluids in High Velocity

  AUTHORS: Thadeu das Neves Conti, Eduardo Lobo Lustosa Cabral, Gaianê Sabundjian

  KEYWORDS: Computational Fluid Mechanics, Compressible Flow, Finite Elements Method, Navier-Stokes Equations, Shock Waves

  JOURNAL NAME: Energy and Power Engineering, Vol.9 No.2, February 17, 2017

  ABSTRACT: This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.