# zbMATH — the first resource for mathematics

Note on the von Neumann stability of explicit one-dimensional advection schemes. (English) Zbl 0848.76061
A number of well-known explicit advection schemes are considered and extended to large time step $$\Delta t$$. The analysis also includes a simple interpretation of (large $$\Delta t$$) TVD constraints.

##### MSC:
 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76R99 Diffusion and convection 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
##### Keywords:
Courant number; large time step; TVD constraints
Full Text:
##### References:
 [1] Fletcher, C. A. J.: Computational techniques for fluid dynamics. (1990) · Zbl 0699.65052 [2] Leonard, B. P.: Note on the von neuman stability of the explicit FTCS convective diffusion equation. Appl. math. Modelling 4, 401-402 (1980) · Zbl 0443.76049 [3] Lax, P. D.; Wendroff, B.: Systems of conservation laws. Comm. pure appl. Math. 13, 217-237 (1960) · Zbl 0152.44802 [4] Leith, C. E.: Numerical simulation of the Earth’s atmosphere. Methods comput. Phys. 4, 1-28 (1965) [5] Fromm, J. E.: A method for reducing dispersion in convective difference schemes. J. comput. Phys. 3, 176-189 (1968) · Zbl 0172.20202 [6] Leonard, B. P.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. methods appl. Mech. engrg. 19, 59-98 (1979) · Zbl 0423.76070 [7] Sweby, P. K.: High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. anal. 21, 995-1011 (1984) · Zbl 0565.65048 [8] Roache, P. J.: A flux-based modified method of characteristics. Internat. J. Numer. methods in fluids 15, 1259-1275 (1992) · Zbl 0765.76057
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.