Remarks on high-resolution split schemes computation

The high-resolution generalized Riemann problem (GRP) conservation laws scheme for compressible flows combined with Strang-type operator splitting is applied to computing an initial value problem having a discontinuous initial data. Imperfect representation of the initial data on the Cartesian grid, where the smooth curve of discontinuity is approximated by a jagged line, gives rise to spurious waves when using high-resolution integration with operator splitting. The nature of these waves is clarified by comparison to a one-dimensional model. We demonstrate that it is not the operator splitting that gives rise to these waves, but rather the better quality of the hyperbolic (one-dimensional) solver, which is not degraded by the operator splitting. It is expected that this property of retaining sharp features of initial data will also be produced by other second-order conservation laws schemes.