Finite element methods for flow problems with moving boundaries and interfaces

Finite element methods in flow problems, Second International Symposium, Proceedings Conference held at Santa Margharita Ligure, Italy, June 1976. Published by ICCAD, c/o 1st Scienze delle Costruzioni, Via Montallegro 1, 16145 Genova, Italy. $25

Since its introduction in 1991 for computation of flow problems with moving boundaries and interfaces, the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation has been applied to a diverse set of challenging problems. The classes of problems computed include free-surface and two-fluid flows, fluid–object, fluid–particle and fluid–structure interaction (FSI), and flows with mechanical components in fast, linear or rotational relative motion. The DSD/SST formulation, as a core technology, is being used for some of the most challenging FSI problems, including parachute modeling and arterial FSI. Versions of the DSD/SST formulation introduced in recent years serve as lower-cost alternatives. More recent variational multiscale (VMS) version, which is called DSD/SST-VMST (and also ST-VMS), has brought better computational accuracy and serves as a reliable turbulence model. Special space–time FSI techniques introduced for specific classes of problems, such as parachute modeling and arterial FSI, have increased the scope and accuracy of the FSI modeling in those classes of computations. This paper provides an overview of the core space–time FSI technique, its recent versions, and the special space–time FSI techniques. The paper includes test computations with the DSD/SST-VMST technique.

Massively parallel finite element simulation of compressible and incompressible flows

It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geometry and eventually convert governing equations into finite-dimensional algebraic systems. To date, many attempts have been made by exploiting machine learning to solve flow problems. However, conventional data-driven machine learning algorithms require heavy inputs of large labeled data, which is computationally expensive for complex and multi-physics problems. In this paper, we proposed a data-free, physics-driven deep learning approach to solve various low-speed flow problems and demonstrated its robustness in generating reliable solutions. Instead of feeding neural networks large labeled data, we exploited the known physical laws and incorporated this physics into a neural network to relax the strict requirement of big data and improve prediction accuracy. The employed physics-informed neural networks (PINNs) provide a feasible and cheap alternative to approximate the solution of differential equations with specified initial and boundary conditions. Approximate solutions of physical equations can be obtained via the minimization of the customized objective function, which consists of residuals satisfying differential operators, the initial/boundary conditions as well as the mean-squared errors between predictions and target values. This new approach is data efficient and can greatly lower the computational cost for large and complex geometries. The capacity and generality of the proposed method have been assessed by solving various flow and transport problems, including the flow past cylinder, linear Poisson, heat conduction and the Taylor–Green vortex problem.

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

A Scheme for Generating Unstructured Grids on Spheres with Application to Parallel Computation

The harmonic balance method has proven to be an efficient tool for the study of aeroelastic phenomena associated with blades in turbomachinery components. In the turbomachinery industry it is used, for example, to predict the flutter susceptibility of blades using structured meshes. For the analysis of more complex geometries, like cavities or labyrinth seals, unstructured grids are easier to create than structured ones to accurately model geometric details of these components. With this application in mind, specifically the flutter analysis of labyrinth seals, an existing harmonic balance solver for the unsteady Reynolds averaged Navier-Stokes equations on structured grids has been extended to work efficiently on unstructured grids. Although the harmonic balance algorithm itself is agnostic to the spatial discretization method, as it is only related to the discretization in time, some adaptations are necessary for an efficient implementation. To verify the extensions for unstructured grids, the harmonic balance solver is applied to the flutter analysis of a NACA airfoil exhibiting an oscillating shock-induced separation region. To demonstrate the ability to handle unstructured mixed-element grids, a flutter analysis of a generic labyrinth seal test case on an unstructured grid is performed.

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method (FDM) and finite element method (FEM) was developed to analyze the fluid structure interaction (FSI) problem. The FDM, in which the Constraint Interpolation Profile (CIP) method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting (THINC/SW) scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary (IB) method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.

Many open‐channel flow problems may be modeled as depth‐averaged flows. Petrov‐Galerkin finite element methods, in which up‐wind weighted test functions are used to introduce selective numerical dissipation, have been used successfully for modeling open‐channel flow problems. The underlying consistency and generality of the finite element method is attractive because separate computational algorithms for subcritical and supercritical flow are not required and algorithm extension to the two‐dimensional depth‐averaged flow equations is straightforward. Here, a reconsideration of the fundamental role of the characteristics in the determination of the up‐wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov‐Galerkin scheme entitled the characteristic dissipative Galerkin method. A linear stability analysis illustrates the selective damping of short wavelengths and excellent phase accuracy achieved by this scheme, as well as its insensitivity to parameter variation. Numerical tests are also presented to illustrate the rugged performance of the scheme. This method could be extended to other hyperbolic systems such as: two‐dimensional flows, multilayer fluids, or sediment‐transport problems.

An immersed boundary method for fluid-structure interaction based on variational transfer

A strong-coupled method combined finite element method and lattice Boltzmann method via an implicit immersed boundary scheme for fluid structure interaction

Since free surface flows are seen in nature phenomena and artificial systems, the analysis for these flows has been more important in mechanical engineering. However, theoretical analyses are almost impossible because the boundary conditions are nonlinear equations in analyzing the free surface flows. Thus, numerical analyses are needed. Finite element method (FEM) which can be used for unstructured grid can easily treat boundary conditions. Thus, FEM is used in many technological fields. In this thesis, free surface flow problems were analyzed using the finite element method. In solving these problems, an arbitrary Lagrangian-Eulerian (ALE) kinematical description of the fluid domain was adopted, in which the nodal point can be displaced independently of the fluid motion. The ALE method was introduced into the Generalized Simplified Marker and Cell (GSMAC) method. Damping out the alternating errors was examined in this scheme.

Three-dimensional numerical simulations of strongly nonlinear free surface flows are performed by lattice Boltzmann method (LBM), which features a number of performance-related advantages, particularly concerning data locality and parallel computing. A Multi-Passage-Interface (MPI) multicore processors parallelized free surface LBM solver is applied for the present three-dimensional numerical simulations. A Smagorinsky LES turbulent model serves to capture the small-scale turbulent structures of the flow. Experiments on dam breaking from previous articles are used to compare and verify two-dimensional (2D) and three-dimensional (3D) LBM model. A new experimental setup is also developed in order to observe the three-dimensionality effect. The findings demonstrated that the free surface LBM simulation agrees well with the experiments.

In a flow including a free surface, an interaction relationship between objects and the free surface is seen in many cases. In recent years, research on environmental change and protection has become active, so analyzing a flow field including the free surface is one of the major issues in river engineering and marine engineering. However, in most of the previous researches, the flow field was limited to the reproduction of the simple flow field. In this study, we dealt with the flow field including the free surface around a moving object with a complicated shape. So, in order to show the change of the shape of the free surface caused by the moving object, the Interface Tracking method was adopted. In this method, in order to express how the interface moves, it is necessary to move and deform the computational grid. Therefore, the calculation method was constructed based on the Unstructured Moving-Grid Finite-Volume method, which strictly satisfies the geometric conservation law and the physical conservation law. The NACA0012 blade was placed under the free surface, and the relationship between the blade's movement and the free surface was investigated. As a result, it was confirmed that the detail change of the free surface caused by the movement of the blade. Thus, it could be shown the promising feature of the computation.