A spectral multidomain method for the solution of hyperbolic systems
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
Stability analysis of spectral methods for hyperbolic initial-boundary value systems
SIAM Journal on Numerical Analysis
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Time-dependent boundary conditions for hyperbolic systems, II
Journal of Computational Physics
Multidomain spectral solution of the Euler Gas-dynamics equations
Journal of Computational Physics
Multidomain spectral solution of compressible viscous flows
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations
Journal of Computational Physics
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We present a spectral numerical method for solving one-dimensional systems of partial differential equations (PDEs) which arise from linearization of the Euler equations about an exact solution depending on space and time. A two-domain Chebyshev collocation method is used. Matching of quantities is performed in the space of characteristic variables as suggested by Kopriva [Appl. Numer. Math. 2 (1986) 221; J. Comput. Phys. 125 (1996) 244]. Time-dependent boundary conditions are handled following an approach proposed by Thompson [J. Comput. Phys. 68 (1987) 1; 89 (1990) 439]. An exact numerical stability analysis valid for any explicit three-step third-order nondegenerate Runge-Kutta scheme is provided. The numerical method is tested against exact solutions for the three fundamental modes of a compressible flow (entropy, vorticity and acoustic modes).