| dc.description |
Very simple linearisations for the solution to the Riemann problem for the
time-dependent and for the steady supersonic Euler equations are presented.
When used locally in conjunction with Godunov-type methods, computing savings
by a factor of about four, relative to the use of exact Riemann solvers, can
be achieved.
For severe flow regimes however, the linearisation looses accuracy and
robustness. We then propose the use of a Riemann-solver adaptation
procedure.
This retains the accuracy and robustness of the exact Riemann solver and the
computational efficiency of the cheap linearised Riemann solver. Also,
reliable and simple switching criteria are presented. Numerical results for
one, two and three-dimensional test problems suggest that the resulting
numerical methods are competitive for practical applications, in terms
of robustness, accuracy and computational efficiency. |
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