# zbMATH — the first resource for mathematics

A flux-based modified method of characteristics. (English) Zbl 0765.76057
Summary: A flux-based modified method of characteristics (MMOC) methodology in 1D is described which has the following properties: unconditional stability (though explicit), exact answers for integer $$CFL$$ (Courant) numbers, completely conservative (locally and globally) and able to utilize various flux limiters and various characteristic- (trajectory-) tracking algorithms. The use of characteristics based on cell-wise constant characteristic velocities results in considerable code simplification, and van Leer’s MUSCL [B. van Leer, J. Comput. Phys. 32, No. 1, 101- 136 (1979)] is an acurate and cost-effective flux limiter. For $$CFL>1$$ the flux limiter is applied only to the non-integer part of $$CFL$$, whereas the integer part is exact for constant velocities; therefore acuracy improves with larger $$CFL$$. It is not a cheap algorithm, although explicit, because the operation count per time step increases with the integer part of $$CFL$$, but it is much more acurate than the commonly used implicit upstream differencing. This flux-based MMOC method is well suited for groundwater flow calculations in which large local Courant numbers arise owing to grid clustering.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
Full Text: