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A great number of numerical schemes have been developed in recent years
for the simulation of compressible gas dynamics and are available in the
literature. These numerical discretizations differ essentially in the
way they address the very difficult problem concerning the formation of
the flow discontinuities like shocks and contact discontinuities.
This difficulty is of primary
importance because the overall accuracy of these calculations is very
closely related to the accuracy with which flow discontinuities are
represented.
In the development and implementation of ShockLib, we have considered
a high-resolution Godunov-type shock-capturing approach where the
discretization is done directly on the integral formulation of the
conservation laws. All the schemes available here share the following
key ingredients:
- a conservative discretization to ensure a correct shock-capturing
behaviour and convergence in a weak sense;
- a high-order interpolation technique to properly describe the
flow-variables inside any cell and their influence on the
interfaces (flux-calculations)6.1;
- a Riemann Solver to compute fully non-linear wave interactions
and to directly provide upwinding properties in the scheme;
- a separate high-order time-integration method, usually an
explicit multistage Runge-Kutta time-marching scheme.