A Positive Definite Limiter for Advection Problems

Advection schemes are important in many branches of computational fluid dynamics. They are used for tracer transport in atmospheric models, where the tracer mixing ratios must remain positive. Many advection schemes employ monotonic limiters, however these can reduce the accuracy of the schemes for smooth data. In this article a commonly used monotonic limiter is modified to make it positive definite (but not strictly monotonic). Testing in multiple dimensions shows that there is improved accuracy over the monotonic limiter, while no negative values are produced.