High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI. A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme.

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  1. Adler, Michael C.; Gaitonde, Datta V.: Dynamics of strong swept-shock/turbulent-boundary-layer interactions (2020)
  2. Ranadive, Harshad D.; Wang, Haiou; Savard, Bruno; Hawkes, Evatt R.: Assessment of artificial fluid properties for high-order accurate large-eddy simulations of shock-free compressible turbulent flows with strong temperature gradients (2019)
  3. Unnikrishnan, S.; Gaitonde, Datta V.: First-mode-induced nonlinear breakdown in a hypersonic boundary layer (2019)
  4. Adler, Michael C.; Gonzalez, David R.; Stack, Cory M.; Gaitonde, Datta V.: Synthetic generation of equilibrium boundary layer turbulence from modeled statistics (2018)
  5. Hammer, Patrick R.; Visbal, Miguel R.; Naguib, Ahmed M.; Koochesfahani, Manoochehr M.: Lift on a steady 2-D symmetric airfoil in viscous uniform shear flow (2018)
  6. Kozyrakis, G. V.; Delis, A. I.; Kampanis, N. A.: A finite difference solver for incompressible Navier-Stokes flows in complex domains (2017)
  7. Rumpfkeil, Markus P.: Using steady flow analysis for noise predictions (2017)
  8. Barnes, C. J.; Visbal, M. R.; Huang, P. G.: On the effects of vertical offset and core structure in streamwise-oriented vortex-wing interactions (2016)
  9. Motheau, E.; Abraham, J.: A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy (2016)
  10. Yang, Yan; Wan, Minping; Shi, Yipeng; Yang, Kun; Chen, Shiyi: A hybrid scheme for compressible magnetohydrodynamic turbulence (2016)
  11. Hammad, D. A.; El-Azab, M. S.: A (2N) order compact finite difference method for solving the generalized regularized long wave (GRLW) equation (2015)
  12. Poggie, Jonathan; Bisek, Nicholas J.; Gosse, Ryan: Resolution effects in compressible, turbulent boundary layer simulations (2015)
  13. Schmitt, Christoph; Pitsch, Heinz: Reactive linearized equations of perturbed compressible variables for low-Mach number variable-density flows (2015)
  14. Shi, YuFeng; Xu, Biao; Guo, Yan: Numerical solution of Korteweg-de Vries-Burgers equation by the compact-type CIP method (2015)
  15. Shi, YuFeng; Xu, Biao; Guo, Yan: A compact-type CIP method for general Korteweg-de Vries equation (2014)
  16. Inasawa, Ayumu; Asai, Masahito; Nakano, Takuya: Sound generation in the flow behind a rectangular cylinder of various aspect ratios at low Mach numbers (2013)
  17. Rizzetta, D.; Visbal, M.: Plasma flow control simulations of a low-Reynolds number low-aspect-ratio wing (2012)
  18. Fico, Vincenzo; Emerson, David R.; Reese, Jason M.: A parallel compact-TVD method for compressible fluid dynamics employing shared and distributed-memory paradigms (2011)
  19. Kawai, Soshi; Terashima, Hiroshi: A high-resolution scheme for compressible multicomponent flows with shock waves (2011)
  20. Rizzetta, Donald P.; Visbal, Miguel R.: Exploration of plasma-based control for low-Reynolds number airfoil/gust interaction (2011)

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