Date: 12/02/2025 - 12/03/2025

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 truncation 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. Analytical 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 discretization 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 dynamics 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 different 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 developing 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.

Registration is not mandatory but appreciated, as it helps us with organization and catering.

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