Date: 02.12.2025 - 03.12.2025

Organizers: Simon Candelaresi, Christoph Knote, Michael Schlottke-Lakemper

Abstract:

Numerical simulation codes for computational fluid dynamics are almost always
affected by numerical dissipation in the form of numerical viscosity and numerical
diffusion. The source for this error is the numerical method used and its local trun-
cation error. Increased spatial resolution or smaller time steps typically reduce
these artificial numerical errors. While scientists developing and using numerical
codes acknowledge the existence of these errors, their magnitude, behavior with
changing parameters or resolution, and their source, are usually less clear. An-
alytical calculations are possible, but become excessively complex, especially for
implicit methods or anything other than finite difference methods. This limits any
scientists aware of numerical dissipation to numerical experiments to understand
the amount of dissipation in their code. Unfortunately, even this analysis is often
not done.
In this CAAPS Workshop we are aiming to understand the effects, properties
and sources of numerical dissipation in numerical methods that are typically used
in computational fluid dynamics. These methods typically use some spatial dis-
cretization and explicit time integration, like one of the Runge-Kutta methods.
For these methods, it is possible – albeit with some effort – to explicitly calculate
the errors introduced by the numerical approach for a typical fluid or gas dynam-
ics problem. So far this has been done only for the simplest PDEs and simplest
numerical methods. We aim to tackle this oversight in this workshop from dif-
ferent directions. With CAAPS members using different kinds of codes we can
also perform numerical experiments quantifying the numerical dissipation. Simple
problems, like damped waves or diffusion can be easily used.
To achieve all this we are aiming of bringing together experts with different
backgrounds. Those include numerical analysts and scientists using and develop-
ing numerical methods. With this wide range of experience and expertise we can
then tackle the problem of numerical dissipation for a wider range of numerical
methods.