ORDER OF APPROXIMATION, ORDER OF NUMERICAL CONVERGENCE AND OF MULTIDIMENSIONAL GAS-DYNAMICS COMPUTATION EFFICIENCY IN EULERIAN VARIABLES ON THE EXAMPLE OF "BLAST WAVES" PROBLEM CONVERGENCE COMPUTATION
Yu. A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc 2004. Вып.4. С. 51-61.
Computations for convergence of the well known 1D test problem "Blast Waves" over several gas-dynamics difference schemes with different orders of convective item approximation are presented in the paper. It has been established that the order of numerical convergence does not exceed unit, including the Lagrangian case; as for the practically interesting range of grid points the order of Eulerian method convergence is three-fold less than the order of approximation. The example of wrong convergence in the non-conservative case is given. Estimations, that connect the computation expenses (number of calculations) with the required error and difference scheme quality parameters, were obtained by means of 1D computation results extrapolation on 2D and 3D cases. The following conclusions were drawn: (1) difference schemes of Eulerian gas-dynamics with the first order of convective terms approximation should be abandoned; (2) it is reasonable to pass over to difference schemes with higher orders of approximation depending on the required grade of results accuracy. The cross-type difference scheme with artificial anti-dispersion with the phase error of the fourth infinitesimal order is briefly described for the 1D Lagrangian gas-dynamics.
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