Implementation of high-order compact finite-difference method to parabolized Navier-Stokes schemes

Esfahanian, V ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1002/fld.1774
  3. Publisher: 2008
  4. Abstract:
  5. The numerical solution to the parabolized Navier-Stokes (PNS) and globally iterated PNS (IPNS) equations for accurate computation of hypersonic axisymmetric flowfields is obtained by using the fourth-order compact finite-difference method. The PNS and IPNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming type with a high-order compact accuracy. A shock-fitting procedure is utilized in both compact PNS and IPNS schemes to obtain accurate solutions in the vicinity of the shock. The main advantage of the present formulation is that the basic flow variables and their first and second derivatives are simultaneously computed with the fourth-order accuracy. The computations are carried out for a benchmark case: hypersonic axisymmetric flow over a blunt cone at Mach 8. A sensitivity study is performed for the basic flowfield, including profiles and their derivatives obtained from the fourth-order compact PNS and IPNS solutions, and the effects of grid size and numerical dissipation term used are discussed. The present results for the flowfield variables and also their derivatives are compared with those of other basic flow models to demonstrate the accuracy and efficiency of the proposed method. The present work represents the first known application of a high-order compact finite-difference method to the PNS schemes, which are computationally more efficient than Navier-Stokes solutions. Copyright © 2008 John Wiley & Sons, Ltd
  6. Keywords:
  7. Benchmarking ; Computational fluid dynamics ; Difference equations ; Enzymes ; Finite difference method ; Flow fields ; Incompressible flow ; Military operations ; Powders ; Axisymmetric ; Basic flows ; Blunt cones ; Compact finite-difference method ; Difference algorithms ; Fitting procedures ; General curvilinear coordinates ; Grid sizes ; Hypersonic axisymmetric flows ; Iterated PNS (IPNS) equations ; Numerical dissipations ; Numerical solutions ; PNS equations ; Second derivatives ; Sensitivity studies ; Navier Stokes equations
  8. Source: International Journal for Numerical Methods in Fluids ; Volume 58, Issue 6 , 2008 , Pages 659-685 ; 02712091 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/10.1002/fld.1774