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Linear stability condition for explicit Runge–Kutta methods to solve the compressible Navier‐Stokes equations
Author(s) -
Müller Bernhard
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670120205
Subject(s) - mathematics , runge–kutta methods , inviscid flow , mathematical analysis , navier–stokes equations , stability (learning theory) , finite volume method , compressibility , numerical analysis , classical mechanics , physics , machine learning , computer science , mechanics , engineering , aerospace engineering
Abstract A linear stability condition is dervied 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.