Abstract
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.
Original language | English |
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Pages (from-to) | 1008-1015 |
Number of pages | 8 |
Journal | SIAM Journal on Scientific Computing |
Volume | 22 |
Issue number | 3 |
DOIs | |
State | Published - 2001 |
Keywords
- Compressible flow
- Godunov-type scheme
- GRP method
- High-resolution computation
- Irregular cells
- Shock waves