The TRR 181 seminar is held by Dr. Claus Goetz (Universität Hamburg, TP M5) on
Can high order advection schemes reduce spurious mixing in ocean models?
at Universität Hamburg on October 19 at 10 am, Bundesstr. 53, room 22/23 (ground floor).
The linear advection equation is arguably the simplest partial differential equation one could imagine. With sophisticated computational tools at our disposal, it may seem like solving linear advection problems numerically should be a fairly trivial task. However, when dealing with discontinuities in the data, we run into surprisingly tough challenges. Near discontinuities numerical methods are prone to either develop oscillations (which may hurt non-negativity constraints), or smear out the discontinuity, effectively leading to a smooth solution where there should be a jump.
In the context of ocean modeling, such problems can occur in passive tracer transport. Consider, say, data with a jump in salinity. Mass conservation and non-negativity of the salinity are mandatory requirements on our numerical method, but many commonly used methods will then produce an undesired smoothing of the jump. When a numerical scheme is unable to preserve crisp discontinuities, we interpret this as the introduction of spurious mixing in our numerical solution.
In this talk we will explore the possibility of reducing spurious mixing with the help of high order advection schemes. To this end, we give a short introduction to so called high order ADER / WENO methods for linear advection problems and discuss benchmarks for the numerical mixing they introduce.