Albin, Nathan and Bruno, Oscar P. (2011) A spectral FC solver for the compressible Navier–Stokes equations in general domains I: Explicit time-stepping. Journal of Computational Physics, 230 (16). pp. 6248-6270. ISSN 0021-9991 http://resolver.caltech.edu/CaltechAUTHORS:20110725-065924210
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We present a Fourier continuation (FC) algorithm for the solution of the fully nonlinear compressible Navier–Stokes equations in general spatial domains. The new scheme is based on the recently introduced accelerated FC method, which enables use of highly accurate Fourier expansions as the main building block of general-domain PDE solvers. Previous FC-based PDE solvers are restricted to linear scalar equations with constant coefficients. The FC methodology presented in this text thus constitutes a significant generalization of the previous FC schemes, as it yields general-domain FC solvers for nonlinear systems of PDEs. While not restricted to periodic boundary conditions and therefore applicable to general boundary value problems on arbitrary domains, the proposed algorithm inherits many of the highly desirable properties arising from rapidly convergent Fourier expansions, including high-order convergence, essentially spectrally accurate dispersion relations, and much milder CFL constraints than those imposed by polynomial-based spectral methods—since, for example, the spectral radius of the FC first derivative grows linearly with the number of spatial discretization points. We demonstrate the accuracy and optimal parallel efficiency of the algorithm in a variety of scientific and engineering contexts relevant to fluid-dynamics and nonlinear acoustics.
|Additional Information:||© 2011 Elsevier Inc. Received 9 November 2010; revised 16 April 2011; accepted 18 April 2011. Available online 28 April 2011. NA gratefully acknowledges the support of the NSF postdoctoral fellowship. NA and OB gratefully acknowledge support from NSF and AFOSR.|
|Subject Keywords:||Spectral method; Complex geometry; Fourier series; Fourier continuation; Partial differential equation; Compressible Navier-Stokes; Direct numerical simulation; Numerical dispersion|
|Official Citation:||Nathan Albin, Oscar P. Bruno, A spectral FC solver for the compressible Navier-Stokes equations in general domains I: Explicit time-stepping, Journal of Computational Physics, Volume 230, Issue 16, 10 July 2011, Pages 6248-6270, ISSN 0021-9991, DOI: 10.1016/j.jcp.2011.04.023. (http://www.sciencedirect.com/science/article/pii/S0021999111002695)|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||25 Jul 2011 14:40|
|Last Modified:||25 Jul 2011 14:40|
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