Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods

Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow

Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed spectral analysis of the semi-discrete model that reveals the spectral gaps. Based on that, we show the inefficiency of standard time integration schemes expressed by a severe restriction of the CFL number. We then develop the first spatially adaptive projective integration schemes to overcome the prohibitive time step constraints of standard time integration schemes. The new schemes use different time integration methods in different parts of the computational domain, determined by the spatially varying value of the relaxation time. We use our analytical results to derive accurate stability bounds for the involved parameters and show that the severe time step constraint can be overcome. The new adaptive schemes show good accuracy in a numerical test case and can obtain a large speedup with respect to standard schemes.

Flow simulations in rotary volumetric pumps and compressors with the fictitious domain method

An adaptive substepping explicit integration scheme with a novel loading-unloading decision method is developed here for the non-isothermal unified hardening (UH) model. The non-isothermal UH model includes a convex subloading surface in the $$p$$p---$$q$$q plane and a nonconvex subloading surface in the $$p$$p---$$T$$T plane. Because of the convex/nonconvex subloading surfaces, the conventional loading-unloading decision method used in stress integration schemes may lead to incorrect elasticity/elastoplasticity judgements. In addition, the conventional loading-unloading decision method is unable to determine the division point that separates the elastic segment from the elastoplastic segment. A simple but robust method, the double cosine (DC) method, is proposed in this paper to solve loading-unloading decision problems. The proposed DC method is then embedded into an adaptive substepping explicit integration scheme to implement the non-isothermal UH model. The accuracy and efficiency of the DC method are discussed by comparing the method with the conventional loading-unloading decision method (the CV method) and the root-finding loading-unloading decision method (the RF method). The performance of the proposed scheme with the DC method is also discussed.

On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows

IG-DRBEM of three-dimensional transient heat conduction problems

In this article we discuss the fictitious domain solution of the Navier‐Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no‐slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier‐Stokes equations and then to an optimal shape problem for Stokes and Navier‐Stokes flow.

In this paper we are interested in a linear elasticity system modeling the presence of a crack inside a volcano. The traction force on this crack induces discontinuities of the displacement field. The computation of the latter is carried out with a finite element method for which the boundary of the crack is taken into account with a fictitious domain approach; It means that the mesh we consider does not fit to the crack. The interest of this approach lies in a framework where the position and the shape of the crack is lead to evolve, and in that case no re-meshing is required.

SummaryAn adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ–Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ–Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ–Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ–Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ–Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Relative performance of body fitted and fictitious domain simulations of flow through fixed packed beds of spheres

Time adaptive variational integrators: A space–time geodesic approach

The purpose of this paper is to analyze the fluid and moving boundary problem by fictitious domain method with Lagrange multiplier. The incompressible Navier-Stokes equation is used in this paper. To solve this equation, fictitious domain method with Lagrange multiplier is applied. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. In fictitious domain method, this method is not necessary to remeshing. Additionally, the calculation time is decreased, and the amount of memory is reduced. It is necessary to approximate by using interpolation function for the Lagrange multiplier. However, it is dicult to integrate the formula. The Delta function of Dirac is used here. Two kinds of meshes are used for fictitious domain method. One of meshes is used as computational domain, the other is used as a bounded domain. In this research, it is analyzed to move the object by the fluid force (drag force) in 3-dimension. In fictitious domain method, it is easy to obtain the fluid force. Because it is defined the Lagrange multiplier is equal to the traction in each node on a bounded domain. The pressure and flow velocity when the object moves are verified. And advantages of fictitious domain method based on distributed Lagrange multiplier are investigated.

Multi-label active learning for image classification has attracted great attention over recent years and a lot of relevant works are published continuously. However, there still remain some problems that need to be solved, such as existing multi-label active learning algorithms do not reflect on the cleanness of sample data and their ways on label correlation mining are defective. For one thing, sample data is usually contaminated in reality, which disturbs the estimation of data distribution and further hinders the model training. For another, previous approaches for label relationship exploration are purely based on the observed label distribution of an incomplete training set, which cannot provide sufficiently efficient information. To address these issues, we propose a novel adaptive low-rank multi-label active learning algorithm, called LRMAL. Specifically, we first use low-rank matrix recovery to learn an effective low-rank feature representation from the noisy data. In a subsequent sampling phase, we make use of its superiorities to evaluate the general informativeness of each unlabeled example-label pair. Based on an intrinsic mapping relation between the example space and the label space of a certain multi-label dataset, we recover the incomplete labels of a training set for a more comprehensive label correlation mining. Furthermore, to reduce the redundancy among the selected example-label pairs, we use a diversity measurement to diversify the sampled data. Finally, an effective sampling strategy is developed by integrating these two aspects of potential information with uncertainty based on an adaptive integration scheme. Experimental results demonstrate the effectiveness of our approach.

Rotational test spaces for a fully-implicit FVM and FEM for the DNS of fluid-particle interaction

The hybrid spectral difference methods (HSD) for the Laplace and Helmholtz equations in exterior domains are proposed. We consider the fictitious domain method with the absorbing boundary conditions (ABCs). The HSD method is a finite difference version of the hybridized Galerkin method, and it consists of two types of finite difference approximations; the cell finite difference and the interface finite difference. The fictitious domain is composed of two subregions; the Cartesian grid region and the boundary layer region in which the radial grid is imposed. The boundary layer region with the radial grid makes it easy to implement the discrete radial ABC. The discrete radial ABC is a discrete version of the Bayliss–Gunzburger–Turkel ABC without pertaining any radial derivatives. Numerical experiments confirming efficiency of our numerical scheme are provided.