Practical framework for data-driven RANS modeling with data augmentation

Acta Mechanica Sinica - Inspired by the iterative procedure of computing mean fields with known Reynolds stresses (Guo et al., Theor Appl Mech Lett, 2021), we proposed a way to achieve data...     

Correction to: Fast data-driven model reduction for nonlinear dynamical systems

Nonlinear Dynamics -     

An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled, but several essential issues remain that strongly affect the performance. Two problems are studied in the current research: (1) the processing of the Reynolds stress tensor and (2) the coupling method between the machine learning model and flow solver. For the Reynolds stress processing issue, we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress. Then, the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis. An adaptive regularization term is employed to enhance the representation performance. For the coupling issue, an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow. The results have high consistency with the direct numerical simulation true values, which proves the validity of the current approach.     

Non-intrusive data-driven ROM framework for hemodynamics problems

Acta Mechanica Sinica - Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PED) by properly combining the...     

An efficient Tabu-search optimized regression for data-driven modeling

In the past decade, data science became trendy and in-demand due to the necessity to capture, process, maintain, analyze and communicate data. Multiple regressions and artificial neural networks are both used for the analysis and handling of data. This work explores the use of meta-heuristic optimization to find optimal regression kernel for data fitting. It is shown that optimizing the regression kernel improve both the fitting and predictive ability of the regression. For instance, Tabu-search optimization is used to find the best least-squares regression kernel for different applications of buckling of straight columns and artificially generated data. Four independent parameters were used as input and a large pool of monomial search domain is initially considered. Different input parameters are also tested and the benefits of using of independent input parameters is shown.     

Physically constrained data-driven correction for reduced-order modeling of fluid flows

We have recently proposed a data-driven correction reduced-order model (DDC-ROM) framework for the numerical simulation of fluid flows, which can be formally written as follows.

     

基于分层数据搜索的数据驱动算法研究

数据驱动计算力学是一种直接利用材料应力应变数据驱动力学仿真计算的新技术.该方法通过反复遍历数据库,为数据驱动模型中的每一个积分点搜索并匹配最佳应力应变数据,使得在高维度和高密度的大规模数据库时计算效率不高.在此背景下,论文提出一种分层数据搜索方案,替换原有的遍历式数据搜索方式,以提升数据驱动的计算效率.该方案的核心思想是将大规模数据库切割成多层级子数据库,并利用树形搜索原理,减小单次搜索数据的范围,降低数据搜索的时间成本,达到提升计算效率的目的.文中简要介绍了数据驱动计算力学的基本步骤,并给出了分层数据库的构造方案,最后结合算例,讨论了数据库分层数量和分层方式对数据驱动计算效率的影响.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material, without constructing an empirical model of the constitutive relation, to predict an equilibrium state of a structure subjected to a specified external load. Provided that a data set comprising stress–strain pairs of material is available, a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie (Kanno 2021, Jpn. J. Ind. Appl. Math.). From the perspective of physical experiments, stress field cannot be directly measured, while displacement and force fields are measurable. In this study, we extend the previous kernel method to the situation that pairs of displacement and force, instead of pairs of stress and strain, are available as an input data set. A new regularized least-squares problem is formulated in this problem setting, and an alternating minimization algorithm is proposed to solve the problem.     

Stochastic framework for modeling the linear apparent behavior of complex materials: Application to random porous materials with interphases

This paper is concerned with the modeling of randomness in multiscale analysis of heterogeneous materials. More specifically, a framework dedicated to the stochastic modeling of random properties is first introduced. A probabilistic model for matrix-valued second-order random fields with symmetry propertries, recently proposed in the literature, is further reviewed. Algorithms adapted to the Monte Carlo simulation of the proposed representation are also provided. The derivations and calibration procedure are finally exemplified through the modeling of the apparent properties associated with an elastic porous microstructure containing stochastic interphases.     

Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers

Many fluid flows of engineering interest, though very complex in appearance, can be approximated by low-order models governed by a few modes, able to capture the dominant behavior (dynamics) of the system. This feature has fueled the development of various methodologies aimed at extracting dominant coherent structures from the flow. Some of the more general techniques are based on data-driven decompositions, most of which rely on performing a singular value decomposition (SVD) on a formulated snapshot (data) matrix. The amount of experimentally or numerically generated data expands as more detailed experimental measurements and increased computational resources become readily available. Consequently, the data matrix to be processed will consist of far more rows than columns, resulting in a so-called tall-and-skinny (TS) matrix. Ultimately, the SVD of such a TS data matrix can no longer be performed on a single processor, and parallel algorithms are necessary. The present study employs the parallel TSQR algorithm of (Demmel et al. in SIAM J Sci Comput 34(1):206–239, 2012), which is further used as a basis of the underlying parallel SVD. This algorithm is shown to scale well on machines with a large number of processors and, therefore, allows the decomposition of very large datasets. In addition, the simplicity of its implementation and the minimum required communication makes it suitable for integration in existing numerical solvers and data decomposition techniques. Examples that demonstrate the capabilities of highly parallel data decomposition algorithms include transitional processes in compressible boundary layers without and with induced flow separation.     

Correction to: Theoretical modeling and experimental evaluation of a magnetostrictive actuator with radial-nested stacked configuration

Nonlinear Dynamics -     

Practical aspects of p‐multigrid discontinuous Galerkin solver for steady and unsteady RANS simulations

Efficient and robust p‐multigrid solvers are presented for solving the system arising from high‐order discontinuous Galerkin discretizations of the compressible Reynolds‐Averaged Navier–Stokes (RANS) equations. Two types of multigrid methods and a multigrid preconditioned Newton–Krylov method are investigated, and both steady and unsteady algorithms are considered in this paper. For steady algorithms, a new strategy is introduced to determine the CFL number, which has been proved to be critical in achieving the effective and stable convergence for p‐multigrid methods. We also suggest a modified smoothing technique to further improve the efficiency of the algorithms. For unsteady algorithms, special attention has been paid to the cycling strategy and the full multigrid technique, and we point out a significant difference on the parameter selection for unsteady computations. The capabilities of the resulted solvers have been examined by performing steady and unsteady RANS simulations. Comparative assessment in terms of efficiency, robustness, and memory consumption are carried out for all solvers. Copyright © 2015 John Wiley & Sons, Ltd.     

A continuum damage mechanics framework for modeling micro-damage healing

A novel continuum damage mechanics-based framework is proposed to model the micro-damage healing phenomenon in the materials that tend to self-heal. This framework extends the well-known Kachanov’s (1958) effective configuration and the concept of the effective stress space to self-healing materials by introducing the healing natural configuration in order to incorporate the micro-damage healing effects. Analytical relations are derived to relate strain tensors and tangent stiffness moduli in the nominal and healing configurations for each postulated transformation hypothesis (i.e. strain, elastic strain energy, and power equivalence hypotheses). The ability of the proposed model to explain micro-damage healing is demonstrated by presenting several examples. Also, a general thermodynamic framework for constitutive modeling of damage and micro-damage healing mechanisms is presented.     

A unified framework for modeling hysteresis in ferroic materials

This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior.     

A multiscale approach to hybrid RANS/LES wall modeling within a high-order discontinuous Galerkin scheme using function enrichment

We present a novel approach to hybrid Reynolds-averaged Navier-Stokes (RANS)/ large eddy simulation (LES) wall modeling based on function enrichment, which overcomes the common problem of the RANS-LES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (A new approach to wall modeling in LES of incompressible flow via function enrichment. J Comput Phys. 2016;316:94-116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the near-wall area, the Navier-Stokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard high-order polynomial basis resolves turbulent eddies, where the mesh is sufficiently fine and the enrichment automatically computes the ensemble-averaged flow if the LES mesh is too coarse. As a result of the derivation, the RANS model is applied solely to the RANS degrees of freedom, which effectively prevents the typical issue of a log-layer mismatch in attached boundary layers. As the full Navier-Stokes equations are solved in the boundary layer, spatial refinement gradually yields wall-resolved LES with exact boundary conditions. Numerical tests show the outstanding characteristics of the wall model regarding grid independence, superiority compared to equilibrium wall models in separated flows, and achieve a speed-up by two orders of magnitude compared to wall-resolved LES.