Numerical errors in the form of dissipation affect nearly all numerical methods. From capillary flows to astrophysical plasmas, researchers have long reported the presence of unphysical dissipation. Despite the widespread use of numerical simulations, the nature and magnitude of numerical dissipation remain poorly understood. In this workshop (December 2nd to 3rd), we will explore the origins and

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.