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Central Runge-Kutta schemes for stiff balance laws. (English) Zbl 1308.76186

Bonilla, Luis L. (ed.) et al., Progress in industrial mathematics at ECMI 2006. Papers of the 14th European conference of the European Consortium for Mathematics in Industry, Leganés, Madrid, Spain, July 10–14, 2006. Berlin: Springer (ISBN 978-3-540-71991-5/hbk). Mathematics in Industry 12, 226-230 (2008).
Summary: In this work, we propose a new family of high order finite volume methods for stiff balance laws. These methods are characterized by an explicit integration of the nonlinear convective terms, while the possibly stiff source is computed implicitly with a novel approach that avoids cell coupling. For this reason, the methods enjoy a favorable stability restriction, without requiring the solution of large nonlinear systems of equations.
For the entire collection see [Zbl 1124.00010].

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
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