Grid Adjacency-based Dynamic Mode Decomposition for Fluid Dynamics and Fluid-Structure Interaction Applications

  • Gkimisis, Leonidas (Max Planck Institute for Dynamics of Complex Technical Systems)
  • Richter, Thomas (Otto von Guericke University)
  • Benner, Peter (Max Planck Institute for Dynamics of Complex Technical Systems)

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In this work, we present a method for non-intrusive model reduction, applied to fluid dynamics and fluid-structure interaction systems. The approach is based on the a priori known sparsity of the full-order system operators (e.g. of the discretized Navier-Stokes equations), which is dictated by grid adjacency information. In order to enforce this type of sparsity, we solve a "local", regularized least-squares problem for each degree of freedom on a grid, considering only the training data from adjacent nodes, thus making computation and storage of the inferred full-order operators feasible. After constructing the non-intrusive, sparse full-order model, the Proper Orthogonal Decomposition is used for its projection to a reduced dimension subspace. This approach differs from methods where data are first projected to a low-dimensional manifold, since here the inference problem is solved for the original, full-order system.