A python implementation of a MUSCL flux limiter to a shallow ice approximation flow code based on finite differences.
For an overview of possible flux limiter functions (phi) to the MUSCL scheme, see Wikipedia - flux limiter. I have implemented now the Sweby (1984) limiter, which uses a parameter called 'beta'. For 1 <= beta <= 2 the limiter is second order TVD and its end members are equal to the limiter discussed in the paper below. If beta = 1, the Sweby limiter is equal to Roe's minmod limiter and if beta = 2 one gets Roe's superbee limiter.
For more details such as the scientific argument as to why this is a good idea, please consult the accompanying publication by A. H. Jarosch, C. G. Schoof, and F. S. Anslow, "Restoring mass conservation to shallow ice flow models over complex terrain,” The Cryosphere, Vol. 7, Iss. 1, pp. 229-240, 2013.