Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Entropy splitting and numerical dissipation
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
Journal of Computational Physics
Large-Scale Computation of Pseudospectra Using ARPACK and Eigs
SIAM Journal on Scientific Computing
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Optimized prefactored compact schemes
Journal of Computational Physics
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
A Parallel Overset Grid High-Order Flow Solver for Large Eddy Simulation
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Stable and accurate schemes for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Journal of Computational Physics
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
Journal of Computational Physics
A Fast Algorithm for Fourier Continuation
SIAM Journal on Scientific Computing
Approximation error in regularized SVD-based Fourier continuations
Applied Numerical Mathematics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Spatially Dispersionless, Unconditionally Stable FC---AD Solvers for Variable-Coefficient PDEs
Journal of Scientific Computing
Hi-index | 31.45 |
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.