Dissipative two-four methods for time-dependent problems
David Gottlieb, Eli Turkel
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Source: Crossref
Published: Jan 1, 1976
DOI: 10.1090/s0025-5718-1976-0443362-6
Open original source ↗Source abstract
A generalization of the Lax-Wendroff method is presented. This generalization bears the same relationship to the two-step Richtmyer method as the Kreiss-Oliger scheme does to the leapfrog method. Variants based on the MacCormack method are considered as well as extensions to parabolic problems. Extensions to two dimensions are analyzed, and a proof is presented for the stability of a Thommen-type algorithm. Numerical results show that the phase error is considerably reduced from that of second-order methods and is similar to that of the Kreiss-Oliger method. Furthermore, the (2, 4) dissipative scheme can handle shocks without the necessity for an artificial viscosity.
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