Unsteady Metric-based Adaptation via Koopman Expansion of the Feature Field

An unsteady, feature-based grid adaptation approach is proposed that addresses the main drawbacks of the current state of the art, namely, the lack of error control of the unsteady derivative terms, the lack of continuous representation of the mesh metric sensors in time, and the lack of adaptation of the mesh velocity to the dynamic flow features in hypersonic flows, e.g., shocks, mixing layers, and separation regions. A grid adaptation algorithm using Dynamic Mode Decomposition will be implemented and integrated into the existing FUN3D CFD code developed at NASA Langley. The proposed algorithm is implemented in a five step process consisting of: 1) featurization of a sensor field in the flow, 2) mesh tensor metric evaluation, 3) Remeshing of the volume, 4) inner-outer loop synchronization to a consistent time-step, and 5) spatial interpolation of the field variables. The proposed algorithm will be compared against the current state of the art and be demonstrated on an oscillating cylinder in supersonic flow.

The unsteady grid adaption will be of particular interest to the Entry, Descent, and Landing community where unsteady high-speed simulations are very common. Additionally, any NASA application dealing with unsteady flow simulations will benefit from this application. Lastly, the FUN3D team at NASA Langley may be interested since this tool will be developed for FUN3D in Phase I.

Any commercial customers dealing with unsteady flow simulations will find this unsteady grid adaptation algorithm beneficial. As computing power increases so does the ability to simulate fully coupled aeroelastic simulations such as flutter which are inherently unsteady. These types of applications would greatly benefit from unsteady grid adaptation.

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