A flux-based modified method of characteristics

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 is an accurate 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 accuracy 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 accurate 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.