Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
A repair method can be viewed as a way to correct values on a discrete mesh by redistributing the conserved quantity so that conservation and a maximum principle are preserved. The maximum principle is that new values should obey certain upper and lower bounds obtained from old values. In this way not only are non-physical quantities eliminated, but oscillations are reduced (albeit not necessarily eliminated). We therefore seek repair algorithms that can be applied to CFD problems, advection problems, or other situations where values of a discrete variable must be placed in bounds without violating a conservation law and without introducing significant errors in the dynamics.
