×

zbMATH — the first resource for mathematics

The ULTIMATE conservative difference scheme applied to unsteady one- dimensional advection. (English) Zbl 0746.76067

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Van Leer, B.; Van Leer, B., (), 163-168
[2] Van Leer, B., Towards the ultimate conservative difference scheme. II. monotonicity and conservation combined in a second-order scheme, J. comput. phys., 14, 361-370, (1974) · Zbl 0276.65055
[3] Van Leer, B., Towards the ultimate conservative difference scheme. III. upstream-centered finite-difference schemes for ideal compressible flow, J. comput. phys., 23, 263-275, (1977) · Zbl 0339.76039
[4] Van Leer, B., Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, J. comput. phys., 23, 276-299, (1977) · Zbl 0339.76056
[5] Van Leer, B., Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. comput. phys., 32, 101-136, (1979) · Zbl 1364.65223
[6] Roe, P.L., (), 163-193, Pt. 2
[7] Mitchell, A.R., (), 2-14
[8] Leonard, B.P., (), 106-120
[9] Fletcher, C.A.J., ()
[10] Lax, P.D.; Wendroff, B., Systems of conservation laws, Comm. pure appl. math., 13, 217-237, (1960) · Zbl 0152.44802
[11] Leonard, B.P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. methods appl. mech. engrg., 19, 59-98, (1979) · Zbl 0423.76070
[12] Fromm, J.E., A method for reducing dispersion in convective difference schemes, J. comput. phys., 3, 176-189, (1968) · Zbl 0172.20202
[13] Sweby, P.K., High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. numer. anal., 21, 995-1011, (1984) · Zbl 0565.65048
[14] Zalesak, S.T., (), 385
[15] Leonard, B.P., (), 347-378
[16] Chakravarthy, S.R.; Osher, S., High resolution applications of the osher upwind scheme for the Euler equations, AIAA paper 83-1943, (1983)
[17] Leonard, B.P.; Niknafs, H., Cost-effective accurate coarse-grid method for highly convective multi-dimensional unsteady flow, ()
[18] Leonard, B.P.; Niknafs, H., Sharp monotonic resolution of discontinuities without clipping of narrow extrema, Comput. & fluids, 19, 729-766, (1990)
[19] Castro, I.P.; Jones, J.M., Studies in numerical computations of recirculating flows, Internat. J. numer. methods fluids, 7, 793-823, (1987) · Zbl 0628.76068
[20] Leonard, B.P., Simple high accuracy resolution program for convective modeling of discontinuities, Internat. J. numer. methods fluids, 8, 1291-1318, (1988) · Zbl 0667.76125
[21] Leonard, B.P.; Mokhtari, S., Beyond first-order upwinding: the ULTRA-SHARP alternative for nonoscillatory steady-state stimulation of convection, Internat. J. numer. methods engrg., 30, 141-154, (1990)
[22] Gaskell, P.H.; Lau, A.K.C., Curvature compensated convective transport: SMART, a new boundedness preserving transport algorithm, Internat. J. numer. methods fluids, 8, 617-641, (1988) · Zbl 0668.76118
[23] Leonard, B.P., (), 226-233
[24] Leonard, B.P., (), 1-23
[25] Leonard, B.P.; Vachtsevanos, G.J.; Abood, K.A., (), 113-128
[26] Yee, H.C., Upwind and symmetric shock-capturing schemes, Nasa tm-89464, (1987) · Zbl 0621.76026
[27] Roe, P.L.; Baines, M.J., (), 281-290
[28] Roe, P.L.; Baines, M.J., (), 283-290
[29] Roe, P.L., (), 337-365
[30] Gaskell, P.H.; Lau, A.K.C., (), 51-62
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.