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.; Gonzalez, David R.; Stack, Cory M.; Gaitonde, Datta V.: Synthetic generation of equilibrium boundary layer turbulence from modeled statistics (2018)
  2. Kozyrakis, G. V.; Delis, A. I.; Kampanis, N. A.: A finite difference solver for incompressible Navier-Stokes flows in complex domains (2017)
  3. Rumpfkeil, Markus P.: Using steady flow analysis for noise predictions (2017)
  4. 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)
  5. Yang, Yan; Wan, Minping; Shi, Yipeng; Yang, Kun; Chen, Shiyi: A hybrid scheme for compressible magnetohydrodynamic turbulence (2016)
  6. Hammad, D. A.; El-Azab, M. S.: A (2N) order compact finite difference method for solving the generalized regularized long wave (GRLW) equation (2015)
  7. Poggie, Jonathan; Bisek, Nicholas J.; Gosse, Ryan: Resolution effects in compressible, turbulent boundary layer simulations (2015)
  8. Schmitt, Christoph; Pitsch, Heinz: Reactive linearized equations of perturbed compressible variables for low-Mach number variable-density flows (2015)
  9. Shi, YuFeng; Xu, Biao; Guo, Yan: Numerical solution of Korteweg-de Vries-Burgers equation by the compact-type CIP method (2015)
  10. Shi, YuFeng; Xu, Biao; Guo, Yan: A compact-type CIP method for general Korteweg-de Vries equation (2014)
  11. Inasawa, Ayumu; Asai, Masahito; Nakano, Takuya: Sound generation in the flow behind a rectangular cylinder of various aspect ratios at low Mach numbers (2013)
  12. Rizzetta, D.; Visbal, M.: Plasma flow control simulations of a low-Reynolds number low-aspect-ratio wing (2012)
  13. Kawai, Soshi; Terashima, Hiroshi: A high-resolution scheme for compressible multicomponent flows with shock waves (2011)
  14. Rizzetta, Donald P.; Visbal, Miguel R.: Exploration of plasma-based control for low-Reynolds number airfoil/gust interaction (2011)
  15. Sari, Murat; Gürarslan, Gürhan: A sixth-order compact finite difference method for the one-dimensional sine-Gordon equation (2011)
  16. Gürarslan, Gürhan: Numerical modelling of linear and nonlinear diffusion equations by compact finite difference method (2010)
  17. Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjögreen, Björn; Yee, H. C.; Zhong, Xiaolin; Lele, Sanjiva K.: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves (2010)
  18. Kawai, Soshi; Shankar, Santhosh K.; Lele, Sanjiva K.: Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows (2010)
  19. Lo, S.-C.; Blaisdell, G. A.; Lyrintzis, A. S.: High-order shock capturing schemes for turbulence calculations (2010)
  20. Nogueira, X.; Colominas, I.; Cueto-Felgueroso, L.; Khelladi, S.: On the simulation of wave propagation with a higher-order finite volume scheme based on reproducing kernel methods (2010)

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