van Leer, Bram Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme. (English) Zbl 0276.65055 J. Comput. Phys. 14, 361-370 (1974). Summary: Fromm’s second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms. Care is taken to keep the scheme in conservation form. When applied to a quadratic conservation law, the scheme notably yields a monotonic shock profile, with a width of only 112 mesh.Part I, cf. Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Lect. Notes Phys. 18, 163–168 (1973; Zbl 0255.76064). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 346 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 76M20 Finite difference methods applied to problems in fluid mechanics Citations:Zbl 0255.76064 PDF BibTeX XML Cite \textit{B. van Leer}, J. Comput. Phys. 14, 361--370 (1974; Zbl 0276.65055) Full Text: DOI OpenURL References: [1] van Leer, B., (), 163 [2] Lax, P.D.; Wendroff, B., Comm. pure appl. math., 13, 217, (1960) [3] Fromm, J.E., J. computational phys., 3, 176, (1968) [4] Godunov, S.K., Mat. sb., 47, 271, (1959), Cornell Aeronautical Lab. Transl. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.