Adjoint error estimation and spatial adaptivity for EHL-like models

The use of adjoint error estimation techniques is described for a model problem that is a simplified version of an EHL line contact. Quantities of interest, such as friction, may be dependent upon the accuracy of the Solution in some parts of the domain more than in others. The use of an inexpensive extra solve to calculate an adjoint solution is described for estimating the intergrid error in the value of friction calculated, and as a basis for local refinement. It is demonstrated that this enables an accurate estimate for the quantity of interest to be obtained from a less accurate solution of the model problem

A grid-enabled problem solving environment for parallel computational engineering design

This paper describes the development and application of a piece of engineering software that provides a problem solving environment (PSE) capable of launching, and interfacing with, computational jobs executing on remote resources on a computational grid. In particular it is demonstrated how a complex, serial, engineering optimisation code may be efficiently parallelised, grid-enabled and embedded within a PSE. The environment is highly flexible, allowing remote users from different sites to collaborate, and permitting computational tasks to be executed in parallel across multiple grid resources, each of which may be a parallel architecture. A full working prototype has been built and successfully applied to a computationally demanding engineering optimisation problem. This particular problem stems from elastohydrodynamic lubrication and involves optimising the computational model for a lubricant based on the match between simulation results and experimentally observed data

Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations

This paper describes a new software tool that has been developed for the efficient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Specifically, the software is designed to provide optimal computational performance for multiscale problems, which require highly stable, implicit, time-stepping schemes combined with a parallel implementation of adaptivity in both space and time. By combining these implicit, adaptive discretizations with an optimally efficient nonlinear multigrid solver it is possible to obtain computational solutions to a very high resolution with relatively modest computational resources. The first half of the paper describes the numerical methods that lie behind the software, along with details of their implementation, whilst the second half of the paper illustrates the flexibility and robustness of the tool by applying it to two very different example problems. These represent models of a thin film flow of a spreading viscous droplet and a multi-phase-field model of tumour growth. We conclude with a discussion of the challenges of obtaining highly scalable parallel performance for a software tool that combines both local mesh adaptivity, requiring efficient dynamic load-balancing, and a multigrid solver, requiring careful implementation of coarse grid operations and inter-grid transfer operations in parallel

Three dimensional thermal-solute phase field simulation of binary alloy solidification

We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three scalar field variables. The mathematical model represents the non-isothermal solidification of a metal alloy into a melt substantially cooled below its freezing point at the microscale. Underlying physical molecular forces are captured at this scale by a specification of the energy field. The time rate of change of the temperature, alloy concentration and an order parameter to govern the state of the material (liquid or solid) are controlled by the diffusion parameters and variational derivatives of the energy functional. The physical problem is important to material scientists for the development of solid metal alloys and, hitherto, this fully coupled thermal problem has not been simulated in three dimensions, due to its computationally demanding nature. By bringing together state of the art numerical techniques this problem is now shown here to be tractable at appropriate resolution with relatively moderate computational resources

Comparison of numerical simulations of barrier membranes with impermeable flakes

Steady-state permeation through membranes filled with impermeable flakes has been simulated numerically using a three-dimensional finite element solver. These numerical results are compared to other published numerical results and the equations that are commonly used to estimate the increased membrane resistance. We discuss the conditions for which these equations fail to give good predictions and why. In comparison with other numerical results, predictions of barrier function by the published Monte Carlo simulations are of variable quality in both two and three dimensions. We present a rationale for layer independence of the results and the implications this has on both the design of membranes and how many layers are needed to produce a layer-independent result

Comparison of numerical simulations of barrier membranes with impermeable flakes

Steady-state permeation through membranes filled with impermeable flakes has been simulated numerically using a three-dimensional finite element solver. These numerical results are compared to other published numerical results and the equations that are commonly used to estimate the increased membrane resistance. We discuss the conditions for which these equations fail to give good predictions and why. In comparison with other numerical results, predictions of barrier function by the published Monte Carlo simulations are of variable quality in both two and three dimensions. We present a rationale for layer independence of the results and the implications this has on both the design of membranes and how many layers are needed to produce a layer-independent result

Reliable performance prediction for parallel scientific software in a multi-cluster grid environment

We propose a model for describing and predicting the performance of practical parallel engineering numerical software on a multi-cluster environment with different distributed memory architectures. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors of a given parallel system, by only benchmarking the code on small numbers of processors. The model is tested using a a practical engineering multilevel code. Despite its simplicity the model demonstrates to be accurate and robust with respect the cluster architectures considered