Local mesh adaptation technique for front tracking problems

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh–Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data. © 1998 John Wiley & Sons, Ltd.     

Adjoint‐based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods

We present a robust and efficient target‐based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection–diffusion problems, including the compressible Euler and Navier–Stokes equations. The hybridization of finite element discretizations has the main advantage that the resulting set of algebraic equations has globally coupled degrees of freedom (DOFs) only on the skeleton of the computational mesh. Consequently, solving for these DOFs involves the solution of a potentially much smaller system. This not only reduces storage requirements but also allows for a faster solution with iterative solvers. The mesh adaptation is driven by an error estimate obtained via a discrete adjoint approach. Furthermore, the computed target functional can be corrected with this error estimate to obtain an even more accurate value. The aim of this paper is twofold: Firstly, to show the superiority of adjoint‐based mesh adaptation over uniform and residual‐based mesh refinement and secondly, to investigate the efficiency of the global error estimate. Copyright © 2014 John Wiley & Sons, Ltd.     

Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

Nowadays, aerodynamic computational modeling is carried out on a daily basis in an industrial setting. This is done with the aim of predicting the performance and flow characteristics of new components. However, limited resources in terms of time and hardware force the engineer to employ relatively coarse computational grids, thus achieving results with variable degree of inaccuracy. In this article, a novel combination of feature and adjoint‐based mesh adaptation methods is investigated and applied to typical three‐dimensional turbomachinery cases, such as compressor and fan blades. The proposed process starts by employing feature‐based mesh movement to improve the global flow solution and then adjoint refinement to tune the mesh for each quantity of interest. Comparison of this process with one utilizing only the adjoint refinement procedure shows significant benefits in terms of accuracy of the performance quantity.     

Anisotropic adaptive stabilized finite element solver for RANS models

Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge‐based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A variational multiscale‐stabilized finite element method is used to solve the incompressible Navier‐Stokes equations. Finally, the Spalart‐Allmaras turbulence model is solved using the streamline upwind Petrov‐Galerkin method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases.     

Godunov‐type adaptive grid model of wave–current interaction at cuspate beaches

This paper presents a second‐order accurate Godunov‐type numerical scheme for depth‐ and period‐averaged wave–current interaction. A flux Jacobian is derived for the wave conservation equations and its eigensystem determined, enabling Roe's approximate Riemann solver to be used to evaluate convective fluxes. Dynamically adaptive quadtree grids are used to focus on local hydrodynamic features, where sharp gradients occur in the flow variables. Adaptation criteria based on depth‐averaged vorticity, wave‐height gradient, wave steepness and the magnitude of velocity gradients are found to produce accurate solutions for nearshore circulation at a half‐sinusoidal beach. However, the simultaneous combination of two or more separate criteria produces numerical instability and interference unless all criteria are satisfied for mesh depletion. Simulations of wave–current interaction at a multi‐cusped beach match laboratory data from the United Kingdom Coastal Research Facility (UKCRF). A parameter study demonstrates the sensitivity of nearshore flow patterns to changes in relative cusp height, angle of wave incidence, bed roughness, offshore wave height and assumed turbulent eddy viscosity. Only a small deviation from normal wave incidence is required to initiate a meandering longshore current. Nearshore circulation patterns are highly dependent on the offshore wave height. Reduction of the assumed eddy viscosity parameter causes the primary circulation cells for normally incident waves to increase in strength whilst producing rip‐like currents cutting diagonally across the surf zone. Copyright © 2004 John Wiley & Sons, Ltd.     

Contrast Adaptation Effects under Interocular Suppression for Normal and Strabismic Observers

Our vision system receives two different images from our two eyes. Since these two images usually have high correlation they are fused into a single stable image. In binocular rivalry suppression a stimulus presented in one eye is suppressed and a different stimulus in the other eye is perceived for a certain time interval. For strabismic observers the suppression is continuous between different retinal images caused by misalignment of eye positions. Previous research investigated the effects of this binocular rivalry suppression on a number of visual processes. The present study looked at the effects of contrast adaptation for the adaptation stimulus presented to eyes under interocular suppression. We compared normal and strabismic observers and found that in both types, regardless of the existence of suppression, there was the effect of contrast adaptation. These findings provide evidence that the suppression occurs at a site in the visual system after the locus of contrast adaptation. The contrast adaptation strength differed in the two types of observers.     

A parallel unstructured dynamic mesh adaptation algorithm for 3‐D unsteady flows

An unstructured dynamic mesh adaptation and load balancing algorithm has been developed for the efficient simulation of three‐dimensional unsteady inviscid flows on parallel machines. The numerical scheme was based on a cell‐centred finite‐volume method and the Roe's flux‐difference splitting. Second‐order accuracy was achieved in time by using an implicit Jacobi/Gauss–Seidel iteration. The resolution of time‐dependent solutions was enhanced by adopting an h‐refinement/coarsening algorithm. Parallelization and load balancing were concurrently achieved on the adaptive dynamic meshes for computational speed‐up and efficient memory redistribution. A new tree data structure for boundary faces was developed for the continuous transfer of the communication data across the parallel subdomain boundary. The parallel efficiency was validated by applying the present method to an unsteady shock‐tube problem. The flows around oscillating NACA0012 wing and F‐5 wing were also calculated for the numerical verification of the present dynamic mesh adaptation and load balancing algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

TESPDA-SEI: Tensor embedding substructure preserving domain adaptation for specific emitter identification

For the specific emitter identification (SEI) with few or no labels, domain adaptation make the model respond quickly with the help of empirical information. However, the more extreme case is that there are so few labeled samples in the source domain that it is difficult to train an excellent recognition model. In fact, it is more valuable to make full use of these limited label information. This work aims at proposing an unsupervised domain adaptation (UDA)-based method to accommodate the typical case of no labels in the target domain and small samples in the source domain when new devices are first introduced. The basic principle is to learn tensor embedding shared feature space and preserving inter-class substructure, which perform feature space mapping under the joint source and target domain led by mapping error minimize in the source domain. Specifically, this tensor embedding substructure preserving domain adaptation (TESPDA) consist of three parts, tensor invariant subspace learning, substructure preserving feature space mapping and pseudo-label prediction, which are used to learn inter-class substructure after tensor space mapping and identify the predict labels for the target domain. Finally, experiments are conducted on the real-word ADS-B dataset to demonstrate the effectiveness of the TESPDA method.     

Comparison of hybrid and standard discontinuous Galerkin methods in a mesh-optimisation setting

This paper assesses the benefits of hybridization on the accuracy and efficiency of high-order discontinuous Galerkin (DG) discretizations. Two hybridized methods are considered in addition to DG: hybridized DG (HDG) and embedded DG (EDG). These methods offer memory and computational time savings by introducing trace degrees of freedom on faces that become the only globally-coupled unknowns. To mitigate the effects of solution singularities on accuracy, the methods are compared in an adaptive setting on meshes optimised for the accurate prediction of chosen scalar outputs. Compressible flow results for the Euler and Reynolds-averaged Navier-Stokes equations demonstrate that the hybridized methods offer cost savings relative to DG in memory and computational time. In addition, for the cases tested, EDG yields the lowest error levels for a given number of degrees of freedom. These benefits disappear on uniformly-refined meshes, indicating the importance of using order-optimised meshes when comparing the discretizations.