Abstract
A one-parameter family of second-order explicit and implicit total variation diminishing (TVD) schemes is reformulated so that a simplier and wider group of limiters is included. The resulting scheme can be viewed as a symmetrical algorithm with a variety of numerical dissipation terms that are designed for weak solutions of hyperbolic problems. This is a generalization of Roe and Davis’s recent works to a wider class of symmetric schemes other than Lax-Wendroff. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step.
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© 1986 Springer-Verlag New York Inc.
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Yee, H.C. (1986). Construction of a Class of Symmetric TVD Schemes. In: Dafermos, C., Ericksen, J.L., Kinderlehrer, D., Slemrod, M. (eds) Oscillation Theory, Computation, and Methods of Compensated Compactness. The IMA Volumes in Mathematics and Its Applications, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8689-6_16
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DOI: https://doi.org/10.1007/978-1-4613-8689-6_16
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