What is it about?
For wave propagation problems, numerical errors often stem from inaccurate representations of the dispersion relation of the original problem. Some remedies exist far away from domain boundaries. Here, we provide a solution in terms of Summation-by-Parts (SBP) operators that can be used both near and far from boundaries and interfaces and are guaranteed to be stable and accurate.
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Why is it important?
We find through a series of numerical experiments that the new SBP-operators are superior to classical alternatives for a range of problems involving high-frequency waves, numerical reflection, transition to turbulence and long-time modelling. Thus, the new operators provide a useful tool for many simulations of realistic phenomena that may considerably improve the efficiency of numerical solvers without jeopardising numerical stability.
Perspectives
These new operators are really nice to see in action. For simple problems, such as the advection equation, they provide clear insight into the origins of numerical errors and how to effectively remove these. For more complex problems such as the Taylor-Green vortex, it is an interesting topic to investigate and compare the error contributions from dispersive sources and dissipative sources, and to see how one becomes dominant over the other as the mesh refinement is changed. Many new insights can be and have been made from these comparisons.
Mr Viktor Linders
Linkopings universitet
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This page is a summary of: Summation-by-Parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations, January 2016, American Institute of Aeronautics and Astronautics (AIAA),
DOI: 10.2514/6.2016-1329.
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