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Wave propagation methods for conservation laws with source terms. (English) Zbl 0927.35062
Fey, Michael (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the 7th international conference, Zürich, Switzerland, February 1998. Vol. II. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 130, 609-618 (1999).
The authors investigate Euler equations with source terms near quasi-steady state solutions. The solutions occur e.g. in a fluid in hydrostatic balance in which the flux produced by the pressure is nearly balanced by the gravitational source term. Fractional step methods which split the problem into a homogenuous Riemann subproblem and an ODE subproblem dealing with the source term work quite well for flows away from steady states. In order to capture quasi-steady states the authors developed in an earlier article a high-resolution wave propagation method which incorporates the source term into the Riemann problem. In this article this method is applied to one and two space dimension Euler equations. The numerical results are compared to the results of the Strang splitting method.
For the entire collection see [Zbl 0911.00029].

MSC:
35L65 Hyperbolic conservation laws
35A35 Theoretical approximation in context of PDEs
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