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Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme. (English) Zbl 0276.65055
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).

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
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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.
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