Abstract:
Several explicit second- and higher-order difference schemes for the hyperbolic
conservation laws with the use of the expansions of grid functions in
Lagrange–Burmann series are proposed. Based on the numerical results
for a number of one- and two-dimensional test problems, it is shown
that, in the case of the Euler equations of an inviscid compressible gas,
the quasimonotone profiles of the numerical solutions can be obtained. When
solving the steady two-dimensional problems by the pseudo-unsteady method,
the proposed schemes require the CPU time smaller than in the case of the known
TVD schemes by a factor of six.