On the accuracy of bicompact schemes as applied to computation of unsteady shock waves. (English. Russian original) Zbl 1460.76643
Comput. Math. Math. Phys. 60, No. 5, 864-878 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 5, 884-899 (2020).
Summary: Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system. It is shown that a nonmonotone bicompact scheme has a higher order of convergence in domains of influence of unsteady shock waves. If spurious oscillations are suppressed by applying a conservative limiting procedure, then the bicompact scheme, though being high-order accurate on smooth solutions, has a reduced (first) order of convergence in the domains of influence of shock waves.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
quasilinear hyperbolic system; conservation law; shallow water equations; local convergence; integral convergenceReferences:
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