High Performance Computing of an Industrial Problem in Tribology

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them. The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception. Since this kind of instability problem has both the conventional (i.e. trivial) and the unconventional (i.e. nontrivial) solutions, it is necessary to examine the effects of different numerical algorithms, which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks. Toward this goal, two different numerical algorithms associated with the commonly-used finite element method are considered in this paper. In the first numerical algorithm, the porosity, pore-fluid pressure and acid/solute concentration are selected as basic variables, while in the second numerical algorithm, the porosity, velocity of pore-fluid flow and acid/solute concentration are selected as basic variables. The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks. The related computational simulation results have demonstrated that: 1) the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems. 2) The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation. 3) The extra differential operation is the main source to result in the failure of the second numerical algorithm.

Big Data analyzes correlations from huge raw data and predicts outcomes. It has great impacts on scientific discoveries and value creation. High Performance Computing (HPC) uses parallel processing and advanced programs or software packages to complete complicated jobs quickly. Finite Element Method (FEM) is very powerful in scientific computation and engineering analysis. It has created huge values in almost every area of engineering. In a lot of applications, Finite Element Analysis (FEA) strongly relies on advanced computer technology and HPC. Big Data will play an important role in FEA and HPC. This paper presents confluences among Big Data, FEA and HPC.

The handling and control of towed cable and body systems onboard surface ships and submarines presents a significant technical challenge to design engineers in the defense and ocean industries. The current approaches rely heavily on the empirical methods and the time-consuming and costly prototype testing. Computer simulation provides a cost effective way to reduce the high risks associated with the towed cable/body system. However, the current dynamic analysis of towed cables is mostly done by the finite difference (FD) method in stead of the finite element (FE) method that is widely used in almost all engineering fields. This paper presents an alternative FE method to simulate the dynamics of towed cable and body system, in which the large rigid body motion is coupled with small elastic deformation. The newly derived FE method is formulated in terms of element nodal positions, which is different from the existing FE methods that use displacements. The alternative FE method solves for the cable position directly in order to eliminate accumulated numerical errors arising from existing FE methods that solve for displacements first in order to obtain the cable position over very long period of time. The alternative FE formulation is implemented and applied to real applications to demonstrate its robustness by comparing simulation results with the experimental and sea trial data.

Video-based free-viewpoint rendering from multiple view video capture has achieved video-realistic performance replay. Existing free-viewpoint rendering approaches require storage, streaming and re-sampling of multiple videos, which requires high bandwidth and computational resources limiting applications to local replay on high-performance computers. This paper introduces a layered texture representation for efficient storage and view-dependent rendering from multiple view video capture whilst maintaining the video-realism. Layered textures re-sample the captured video according to the surface visibility. Prioritisation of layers according to surface visibility allows the N-best views for all surface elements to be pre-computed significantly reducing both storage and rendering cost. Typically 3 texture map layers are required for free-viewpoint rendering with an equivalent visual quality to the multiple view video giving a significant reduction in storage cost. Quantitative evaluation demonstrates that the layered representation achieves a 90% reduction in storage cost and 50% reduction in rendering cost without loss of visual quality compared to storing only the foreground of the original multiple view video. This reduces the storage and transmission cost for free-viewpoint video rendering from eight cameras to be similar to the requirements for a single video. Streaming the layered representation enables, for the first time, demonstration of free-viewpoint video rendering on mobile devices and web platforms.

Summary form only give. Due to the growing research in nano technology, the requirement of numerical tools becomes demanding for accurate and fast design. The shrinking electronic or optical devices have brought intense computational burden than ever for the accuracy-concerned refined computational meshes. Based on the above reason, high performance computers are needed to achieve multiple design tasks. At present, there are couple electromagnetic simulators available for the design of nano or THz devices. However, the performance of different algorithms may differ a lot. In this work, the performance of open-source parallel Finite-Difference Time-Domain (FDTD) software on supercomputer Eos and Ranger and the performance of a Finite Element Method (FEM) package on a single workstation are compared for plasmonic waveguide mode coupling simulation (Fig. 1). It is shown that, for the difference of numerical algorithms and material boundary treatment between FDTD and FEM, FEM performs better than FDTD for our design problem. For FDTD, the dimension of the computational window is 15.5 × 10 (all physical parameters are normalized so no unit is described) and the total number of grids is 6,200,000. Due to the nature of FDTD, long-time iteration is required to achieve numerical stability and accuracy. Table I lists the wall clock time Eos took for each submitted job with different core number requested. Based on this statistics, the simulation time cannot be reduced further with more than 96 cores. On the other hand, for the same problem, the simulation widow for FEM is also 15.5 × 10. However, the number of unknown used here is only 159,512 (~1/40 of the number used in FDTD) to achieve required accuracy and stability and the computation time is less than 1 minute.

The parallelization of the finite element method (FEM) is considered. The parallel versions of the FEM package are developed on the base of the sequential version. The elasto-plastic behaviour of the geotechnical structure can be modeled, calculated and analyzed by the package. The Cray Fortran compiler directives are used for the parallelization of source code. The supercomputer SUN E10000 HPC is used for package test. As the engineering example of the geotechnical problem the dam building is modeled, calculated and analyzed. The different versions of parallel FEM package are compared by the reached speed-up.

Real-world groundwater modeling deals with heterogeneous and anisotropic aquifer systems. Numerical models, particularly the finite difference and finite element methods, are extensively used for modeling such a complex aquifer system. The finite difference method is an age-old straightforward approach, whereas the finite element method is more idealistic, relatively new, and has emerged as a popular approach. The unique advantages with the finite element method are (i) an irregular-shaped domain can be discretized into elements with a matching boundary, (ii) a node can be connected with the neighboring nodes in any direction. Thus, the finite element analysis allows water/solute to flow more freely toward the surrounding nodes along nodal links. On the other hand, the mathematical formulation of the finite element technique follows a set of rules step by step. Conventionally, this idealistic approach uses shape functions and integration techniques to develop element matrices, which, in turn, are assembled to form the global matrix. This conventional global matrix was found to be inconsistent with the basic partial differential equation representing the mass balance in a nodal domain as a control volume. As a result, the matrix solution, particularly for nonlinear problems (e.g., vadose zone flow, density dependent flow, and so forth) becomes unstable and computationally burdensome. To overcome the limitations of the conventional finite element method for real-world groundwater modeling, a new approach, called the direct-formulation finite element (DFFE) method, has been developed. In this approach, a two-dimensional model domain is discretized into triangular elements. Element matrices are formed directly based on flow principles and material properties of elements without using shape functions and integration process. The DFFE method is robust. The global matrix is consistent, and the solution is stable and efficient. The results obtained from this approach were found in a good agreement with that obtained from analytical and other widely used models.

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.

Finite element approximation of a nonlinear heat conduction problem in anisotropic media

The general framework of this paper is in the field of numerical simulation of asperity crushing. Different material forming processes, such as strip-rolling and deep drawing, imply mixed lubrication. In this lubrication regime, two types of contact are present at the same time: a direct contact between the two solids at the asperity level and also valleys filled with pressurized oil. Theses contact conditions have a large influence on friction and wear taking place during the upsetting process. As this mixed type of contact is not yet fully understood from the physics point of view, numerical models are essential to achieve a better understanding. For example, semi-analytical asperity crushing models have been developed by Wilson&Sheu [1] and Sutcliffe [2] to take into account the influence of bulk plastic deformations on asperity crushing. The finite element method has also been used to model asperity crushing. Ike&Makinouchi [3] studied the behavior of 2D triangular-shaped asperities under different boundary conditions. Krozekwa et al. [4] modeled 3D triangular asperities behavior, for various bulk strain directions. More recently, Lu et al. [5] compared experimental results of pyramid-shaped asperity and ridge-shaped asperity crushing with finite element simulation results. As in the three former references mentioned above, it has been decided, to study the interaction between a rigid plane and a simplified geometry asperity without lubricant. In this article, numerical asperity crushing results obtained with Metafor[6], a home made large strains software, will be presented. Those results will illustrate the influence of boundary conditions, contact pressure, large bulk strain and geometry of asperities on the evolution of the contact area. As the asperity crushing behaviour is known to be very sensitive to the boundary conditions, in this article, we will also present results using boundary conditions from a cold rolling model named MetaLub. MetaLub [7-8] is a software developed at the University of Liege in partnership with ArcelorMittal R&D center. It iteratively solves the equations resulting from the discretisation using the slab method of the strip coupled to a mixed lubrication model at the interface. This lubrication model takes into account the evolution of the oil film thickness as well as the asperity crushing along the roll bite. We will compare the evolution of the relative contact area obtained with MetaLub to the results obtained with finite elements simulations using the same boundary conditions. [1] Wilson, W.R.D and Sheu, S. Real area of contact and boundary friction in metal forming. Int. J. Mech. Sci. 1988, 30(7), 475-489. [2] Sutcliffe, M.P.F Surface asperity deformation in metal forming processes. Int. J. Mech. Sci., 1988, 30(11), 847-868. [3] Ike, H. and Makinouchi, A. Effect of lateral tension and compression on plane strain flattening processes of surface asperities lying over a plastically deformable bulk. Wear, 1990, 140, 17-38. [4] Korzekwa, D.A., Dawson, P.R. and Wilson W.R.D., Surface asperity deformation during sheet forming. Int. J. Mech. Sci., 1992, 34(7), 521-539. [5] Lu, C., Wei, D., Jiang, Z., and Tieu, K., Experimental and theoretical investigation of the asperity flattening process under large bulk strain, Proc. Inst. Mech. Eng. J. 222 (2008), 271–278. [6] LTAS-MN2L. ULg. http://metafor.ltas.ulg.ac.be/. [7] Stéphany, A., Contribution à l’étude numérique de la lubrification en régime mixte en laminage à froid. PhD dissertation (in French), Université de Liège (2008) [8] Carretta, Y., Stephany, A., Legrand, N., Laugier, M., and Ponthot, J.-P., MetaLub – A slab method software for the numerical simulation of mixed lubrication regime. Application to cold rolling. In Proceedings of the 4th International Conference on Tribology In Manufacturing Processes (ICTMP), 2010,799-808.

Some Adaptive Numerical Technology for Computational Aerodynamics

A finite element–boundary element method for advection–diffusion problems with variable advective fields and infinite domains

The scientific basis of orthodontics is physics and Newtonian mechanics applied to the tooth-periodontal ligament-bone biologic system. The mechanical response of the periodontal ligament (PDL) to forces has a significant impact on bone remodelling and tooth movement. At the early stages, orthodontists mainly evaluated the PDL mechanical properties by in vitro experiments, which guided the use of forces in the orthodontic process. With the development of computers, finite element (FE) methods were increasingly used in the study of orthodontics. The phenomena and results of PDL mechanical tests are abstracted into constitutive equations. The identified constitutive equations are then implemented in finite element software. The finite element method could be used to simulate in vitro and in vivo experiments and predict the response of PDL under various complex working conditions. A visco-hyperelastic constitutive model is proposed and implemented in finite element technique based on prior static mechanical experiments of human PDL. Some complex experimental conditions are simulated to discuss the properties of the constitutive model.

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.