A time-spectral approximate Jacobian based linearized compressible Navier-Stokes solver for high-speed boundary-layer receptivity and stability

Anthony P. Haas, Oliver M.F. Browne, Hermann F. Fasel, Christoph Brehm

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A numerical method for conducting linear receptivity and stability investigations of high-speed wall-bounded flows based on the linearized compressible Navier-Stokes equations is presented. The current approach is directly applicable for stability investigations of arbitrarily complex geometries. The left-hand-side operator for the linear system of equations is obtained by computing numerical right-hand-side Jacobians while the right-hand-side is build from exact flux Jacobians. Utilizing the numerical right-hand-side Jacobian approach avoids lengthy, error prone derivation of the stability equations in the context of generalized curvilinear coordinates. The governing equations are solved using either time-stepping or time-spectral discretizations. Three different time-spectral approaches, i.e., direct inversion, unfactored and factored schemes, are presented and their numerical characteristics for the solution of the linearized Navier-Stokes equations for linear receptivity and stability analysis for large-scale transition problems are explored. Linear receptivity and stability calculation results are provided for different solver options. Performance comparison of the three schemes are presented for a wide range of test cases: An incompressible cross-flow for a swept flat plate boundary layer, a supersonic shock-boundary-layer interaction, hypersonic boundary layers on a flat plate and a flared cone, and, finally, for the receptivity of a hypersonic boundary layer for a right sharp cone.

Original languageEnglish
Article number108978
JournalJournal of Computational Physics
Volume405
DOIs
StatePublished - Mar 15 2020

Bibliographical note

Funding Information:
This work was supported by the U.S. Air Force under a Phase 1 SBIR contract (FA9101-16-M-0044), with Dr. Eric Marineau serving as the Technical Point of Contact. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Air Force or the U.S. Government.

Funding Information:
This work was supported by the U.S. Air Force under a Phase 1 SBIR contract ( FA9101-16-M-0044 ), with Dr. Eric Marineau serving as the Technical Point of Contact. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Air Force or the U.S. Government.

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Boundary-layer stability
  • Hypersonic flows
  • Laminar-turbulent transition
  • Navier-Stokes equations
  • Receptivity
  • Time-spectral

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy (all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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