TY - GEN
T1 - Finite-element solutions to the Reynolds averaged Navier-Stokes equations using a Spalart-Allmaras turbulence model
AU - Burgess, Nicholas K.
AU - Glasby, Ryan S.
AU - Erwin, J. Taylor
AU - Stefanski, Douglas L.
AU - Allmaras, Steven R.
N1 - Publisher Copyright:
© 2017 by Nicholas K. Burgess, Ryan S. Glasby, J. Taylor Erwin, Douglas L. Stefanski, Steven R. Allmaras.
PY - 2017
Y1 - 2017
N2 - The computational fluid dynamics (CFD) literature now fully recognizes that certain finite-element discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations (closed with a turbulence model), routinely encounter non-physical states on under-resolved meshes and during their path to non-linear convergence. This work presents a formulation of the Spalart-Allmaras (S-A) turbulence model that is designed to be stable and robust to these non-physical states (negative values of given turbulence working variable). This work outlines the design and testing of the negative S-A turbulence model (S-A-neg), which is particularly well suited for arbitrarily high-order finite-element discretizations. This S-A-neg model is designed to be energy stable as well as mitigate the non-linearity of the previously derived negative continuation source and diffusion operators. Additionally, this negative continuation of the S-A model reduces to the original model in properly resolved regions of the flow, where the solution to the turbulence-working variable is positive. Numerical examples carried out using both continuous- and discontinuous-finite-element methods are used to demonstrate that this variant of the S-A model is robust for finite-element discretizations.
AB - The computational fluid dynamics (CFD) literature now fully recognizes that certain finite-element discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations (closed with a turbulence model), routinely encounter non-physical states on under-resolved meshes and during their path to non-linear convergence. This work presents a formulation of the Spalart-Allmaras (S-A) turbulence model that is designed to be stable and robust to these non-physical states (negative values of given turbulence working variable). This work outlines the design and testing of the negative S-A turbulence model (S-A-neg), which is particularly well suited for arbitrarily high-order finite-element discretizations. This S-A-neg model is designed to be energy stable as well as mitigate the non-linearity of the previously derived negative continuation source and diffusion operators. Additionally, this negative continuation of the S-A model reduces to the original model in properly resolved regions of the flow, where the solution to the turbulence-working variable is positive. Numerical examples carried out using both continuous- and discontinuous-finite-element methods are used to demonstrate that this variant of the S-A model is robust for finite-element discretizations.
UR - http://www.scopus.com/inward/record.url?scp=85017205440&partnerID=8YFLogxK
U2 - 10.2514/6.2017-1224
DO - 10.2514/6.2017-1224
M3 - Conference contribution
AN - SCOPUS:85017205440
T3 - AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting
BT - AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting
PB - American Institute of Aeronautics and Astronautics Inc.
T2 - 55th AIAA Aerospace Sciences Meeting
Y2 - 9 January 2017 through 13 January 2017
ER -