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.
Highlights
IntroductionThe solution of complex problems in fluid mechanics and heat transfer with the use of numerical techniques, known as Computational Fluid Dynamics (CFD), is today a reality due to the development of computers with high velocity and with
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 work develops an application of the hierarchical function expansion method, elaborated by [2], for the solution of Navier-Stokes equations in two dimensions for high velocity compressible flows
Summary
The solution of complex problems in fluid mechanics and heat transfer with the use of numerical techniques, known as Computational Fluid Dynamics (CFD), is today a reality due to the development of computers with high velocity and with. The solution of turbulent flow on wings using high capacity computer in 1960 would consume years of processing with a coast of millions of dollars. This work develops an application of the hierarchical function expansion method, elaborated by [2], for the solution of Navier-Stokes equations in two dimensions for high velocity compressible flows. This method consists on the use of the finite element method with a Petrov-Galerkin formulation and the expansion of the variables in hierarchical functions. The numerical method developed has the great advantage of being able to adapt the degree of polynomial until the necessary value, instead of using extremely refined meshes
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