Linear stability condition for explicit Runge–Kutta methods to solve the compressible Navier-Stokes equations
✍ Scribed by Bernhard Müller
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 435 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
Communicated by W. Tornig
A linear stability condition is derived for explicit Runge-Kutta methods to solve the compressible Navier-Stokes equations by central second-order finite-difference and finite-volume methods. The equations in non-conservative form are simplified to quasilinear form, and the eigenvalues of the resulting coefficient matrices are determined for general co-ordinates. Assuming a well-posed Cauchy problem with constant coefficients, the von Neumann stability analysis yields sufficient stability conditions for viscous-inviscid operator-splitting schemes. They have been applied in computational aerodynamics to solve the compressible Navier-Stokes equations by an unsplit explicit Runge-Kutta finite-volume method.