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Numerical Simulation of Compressible Vortical Flows Using a Conservative Unstructured-Grid Adaptive Scheme†

Published online by Cambridge University Press:  20 August 2015

Giuseppe Forestieri ,
Alberto Guardone ,
Dario Isola ,
Filippo Marulli  and
Giuseppe Quaranta
Giuseppe Forestieri
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy
Alberto Guardone*
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy
Dario Isola
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy
Filippo Marulli
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy
Giuseppe Quaranta
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa, 34, 20156 Milano, Italy
*
Corresponding author.Email:[email protected]
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Abstract

A two-dimensional numerical scheme for the compressible Euler equations is presented and applied here to the simulation of exemplary compressible vortical flows. The proposed approach allows to perform computations on unstructured moving grids with adaptation, which is required to capture complex features of the flow-field. Grid adaptation is driven by suitable error indicators based on the Mach number and by element-quality constraints as well. At the new time level, the computational grid is obtained by a suitable combination of grid smoothing, edge-swapping, grid refinement and de-refinement. The grid modifications—including topology modification due to edge-swapping or the insertion/deletion of a new grid node—are interpreted at the flow solver level as continuous (in time) deformations of suitably-defined node-centered finite volumes. The solution over the new grid is obtained without explicitly resorting to interpolation techniques, since the definition of suitable interface velocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Numerical simulations of the steady oblique-shock problem, of the steady transonic flow and of the start-up unsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately.

Keywords

52B1065D18Moving grid methodconservative interpolation
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 3 , September 2012 , pp. 866 - 884
Copyright
Copyright © Global Science Press Limited 2012

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Footnotes

†

Presented at the 2nd European Seminar on Coupled Problems June 28–July 2, 2010, Pilsen, Czech Republic.

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