Information geometric regularization integrated into finite volume methods handles shocks in Navier-Stokes-like problems with accuracy competitive to WENO and LAD schemes while using fewer operations per step.
Liou, A sequel to AUSM, Part II: AUSM+-up for all speeds, Journal of Computational Physics214(2006) 137–170
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Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier--Stokes-like problems
Information geometric regularization integrated into finite volume methods handles shocks in Navier-Stokes-like problems with accuracy competitive to WENO and LAD schemes while using fewer operations per step.