A recent approach in modelling coherent structures in fluid flows, called Recursive Dynamic Mode Decomposition, is presented on the example of the flow around two square cylinders, where interactions between the wakes occur. The distance between cylinders varies from one to five side lengths of the square, leading to different behaviour of the wake flow. The proposed method is based on the recursive repeating of a three-step procedure: computation of the DMD mode basis, selection of the mode minimizing the defined residual error, and, finally, purging this mode from the flow (the snapshots). RDMD combines the advantages of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). Low residual error, characteristic of POD, and purer frequency content observed in DMD, make this method especially applicable in unsupervised machine learning-based applications, including machine learning control (MLC) of the flows with few dominant frequencies (Brunton and Noack, 2015).

In the present paper the numerical approach for the modeling of the flow past rotating geometries is presented. Practical methods for two cases are described: the one where whole domain is moving with uniform angular velocity, where the rotation might be included in the governing equations only (in the terms related to Coriolis and centrifugal forces), and the one where part of the domain is rotating, whereas another one is stationary. The second case is illustrated by examples describing the steady and transient flow around a rotating propeller and by a centrifugal pump. Simulations are performed using OpenFOAM CFD solver, with the models covering flow rotation: MRF (multiple reference frame) and AMI (arbitrary mesh interface).

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier–Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

The paper aims to build a reduced order model (ROM) of the left and right ventricle of a human heart. The input heart model is build from 3D sets of registered, flexible surface meshes for the left and right ventricle, resulting from the MRI data. Spatial and temporal variables are separated using Proper Orthogonal Decomposition. It enables data reduction and works as a data-driven filter, separating similar and alternative properties of the left and right ventricle movement, which is diagnostically essential in cardiology studies. Each mode can be correlated with a corresponding heart movement. The temporal coefficients reflect the functioning of the heart, and comparing them may reveal and distinguish pathologies. We have proven that complex heart motion can be modeled with relatively small number of degrees of freedom. The model spanned on a few POD modes allows the analysis of the crucial movement data and better identification of possible failures.

SummaryThe method for computation of stability modes for two‐ and three‐dimensional flows is presented. The method is based on the dynamic mode decomposition of the data resulting from DNS of the flow in the regime close to stable flow (fixed‐point dynamics, small perturbations about steady flow). The proposed approach is demonstrated on the wake flows past a 2D, circular cylinder, and a sphere. The resulting modes resemble the eigenmodes computed conventionally from global stability analysis and are used in model order reduction of the flow. The designed low‐dimensional Galerkin model uses continuous mode interpolation between dynamic mode decomposition mode bases and reproduces the dynamics of Navier–Stokes equations. Copyright © 2015 John Wiley & Sons, Ltd.

A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N-1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. RDMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al. 2012) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have pure frequency content while retaining a residual of comparable order as POD. In contrast to DMD with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit cycle resolution from the same snaphots. RDMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, with nonlinear transient dynamics as a niche application.

Reduced order models allow quickly predict fluid behaviour and to better understand flow phenomena. They are the key enablers of closed-loop flow control. In this paper, reduced-order model (ROM) of an incompressible flow around a wall-mounted cylinder is constructed, by means of Galerkin projection of Navier–Stokes equations onto space spanned by the most dominant eigenmodes of dynamic mode decomposition (DMD). Additionally, genetic algorithm-based calibration is applied to improve the predictive performance of the model. The resulting low-dimensional model of the flow consists of six degrees of freedom and precisely reproduces the dynamics of limit cycle oscillations.

In the IDIHOM Project three aeroelastic testcases have been calculated. Two of them - LANN Wing and DLR-F6 wing-body configuration - have been conducted by PUT. The last one, the HART II rotor has been prepared by NLR. Each partner has used different technology and software tools, hence each of the testcases describes the results of the simulation and technology which has been used.

In this paper analysis of scalability of the solver UNS3, dedicated to direct numerical simulation (DNS) of Navier-Stokes equations, is presented.Efficiency of parallel computations has been examined with the use of a PC cluster built by the Division of Virtual Engineering.Tests have been carried out on a different number of partitions, in the range of 1÷80.The test case was steady flow around a wall-mounted circular cylinder with Reynolds number set to the value of Re = 10.The research included the measurement of preparatory time, calculation time, communication time, speedup, core hours and efficiency.

The article presents elastic analogy approach of deformation curvilinear meshes applied in aeroelastic simulations. The details of algorithm used in developed software with the new metrics designated for high-order mesh quality assessment are presented. The article ends the example of LANN wing deformed by featured tool. Presented software allows conducting the aeroelastic simulation based on CFD discontinuous Galerkin High Order solver.

Article presents the development process of aeroelastic system basing on finite volume CFD solver for higher order methods. The main aspect is interpolation tools which allows application of Discontinuous Galerkin solution of CFD solver. There is also described the elastic analogy deformation tool for curvilinear mesh. To summarize, the two testcases of wing and wing-body configuration aircraft are presented.

This article presents application of modal analysis for the computation of biometric data base (3D faces) and extraction of three dimensional geometrical features. Traditional anthropometric database contains information only about some characteristic points recorded as linear or angular dimensions. The current face recognition systems are also based on the two-dimensional information. To increase level of security the methods need to operate on three-dimensional data. In the article authors present of 3D modal analysis, for decomposition, extraction features and individual coding of analyzed objects sets. Authors apply empirical modal analysis PCA (Principal Component Analysis) for 3D data of human faces. Additionally for face recognition, the comparison of reconstruction with different number of modes are presented and discussed.

The post-processing and correlation analysis (like Proper Orthogonal Decomposition) requires the same topology for all objects in the database. Thus, in the case of 3D scanned data, registration is required. One of possible choices is elastic registration based on the known positions of certain markers (features) on the surface of each scanned object.The present paper targets the method of automatic detection of such markers on the scanned human faces and the elastic deformation resulting in the same topology of the triangular meshes after the registration. Resulting data might be analyzed using methods like POD.

Flow-induced de§ections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like §utter or bueting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the §ow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-|delity computations. The motion of the boundary and mesh is de|ned in Arbitrary Lagrangian€ Eulerian (ALE) approach and results in additional convective term in Galerkinsystem. Thedevelopedsystemisdemonstratedontheexample of a §ow around an oscillating wing.

Reduced order models are key enablers of feedback flow control. One of the most popular methods of model order reduction for fluid flows is Galerkin method. It is based on the projection of (approximated) governing equations onto a subspace spanned by mathematical, physical or empirical modes. The right choice of the modal basis has a significant impact on the scope of applicability of the model [6].