Multilevel mesh partitioning for heterogeneous communication networks

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut edge weight in the graph with the aim of minimising the parallel communication overhead, but recently there has been a perceived need to take into account the communications network of the parallel machine. For example the increasing use of SMP clusters (systems of multiprocessor compute nodes with very fast intra-node communications but relatively slow inter-node networks) suggest the use of hierarchical network models. Indeed this requirement is exacerbated in the early experiments with meta-computers (multiple supercomputers combined together, in extreme cases over inter-continental networks). In this paper therefore, we modify a multilevel algorithm in order to minimise a cost function based on a model of the communications network. Several network models and variants of the algorithm are tested and we establish that it is possible to successfully guide the optimisation to reflect the chosen architecture.

Multiphase mesh partitioning for parallel computational mechanics codes

We consider the load-balancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to as the multiphase mesh partitioning strategy to address such issues. The technique is tested on example meshes containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where a standard mesh partitioning approach fails.

Dynamic fluid–structure interaction using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of flutter analysis

Computational modelling of dynamic fluid-structure interaction (DFSI) is problematical since conventionally computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. Hence, progress in modelling the emerging multi-physics problem of dynamic fluid-structure interaction in a consistent manner is frustrated and significant problems in computation convergence may be encountered in transferring and filtering data from one mesh and solution procedure to another, unless the fluid-structure coupling is either one way, very weak or both. This paper sets out the solution procedure for modelling the multi-physics dynamic fluid-structure interaction problem within a single software framework PHYSICA, using finite volume, unstructured mesh (FV-UM) procedures and will focus upon some of the problems and issues that have to be resolved for time accurate closely coupled dynamic fluid-structure flutter analysis.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

Dynamic fluid-structure interaction using finite volume unstructured mesh procedures

A three dimensional finite volume, unstructured mesh method for dynamic fluid-structure interation is described. The broad approach is conventional in that the fluid and structure are solved sequentially. The pressure and viscous stresses from the flow algorithm provide load conditions for the solid algorithm, whilst at the fluid structure interface the deformed structure provides boundary condition from the structure to the fluid. The structure algorithm also provides the necessary mesh adaptation for the flow field, the effect of which is accounted for in the flow algorithm. The procedures described in this work have several novel features, namely: * a single mesh covering the entire domain. * a Navier Stokes flow. * a single FV-UM discretisation approach for both the flow and solid mechanics procedures. * an implicit predictor-corrector version of the Newmark algorithm. * a single code embedding the whole strategy. The procedure is illustrated for a three dimensional loaded cantilever in fluid flow.

Parallel mesh partitioning on distributed memory systems

The problem of deriving parallel mesh partitioning algorithms for mapping unstructured meshes to parallel computers is discussed in this chapter. In itself this raises a paradox - we seek to find a high quality partition of the mesh, but to compute it in parallel we require a partition of the mesh. In fact, we overcome this difficulty by deriving an optimisation strategy which can find a high quality partition even if the quality of the initial partition is very poor and then use a crude distribution scheme for the initial partition. The basis of this strategy is to use a multilevel approach combined with local refinement algorithms. Three such refinement algorithms are outlined and some example results presented which show that they can produce very high global quality partitions, very rapidly. The results are also compared with a similar multilevel serial partitioner and shown to be almost identical in quality. Finally we consider the impact of the initial partition on the results and demonstrate that the final partition quality is, modulo a certain amount of noise, independent of the initial partition.

Dynamic mesh partitioning and load-balancing for parallel computational mechanics codes

In this Chapter we discuss the load-balancing issues arising in parallel mesh based computational mechanics codes for which the processor loading changes during the run. We briefly touch on geometric repartitioning ideas and then focus on different ways of using a graph both to solve the load-balancing problem and the optimisation problem, both locally and globally. We also briefly discuss whether repartitioning is always valid. Sample illustrative results are presented and we conclude that repartitioning is an attractive option if the load changes are not too dramatic and that there is a certain trade-off between partition quality and volume of data that the underlying application needs to migrate.

A finite volume unstructured mesh approach to dynamic fluid–structure interaction: an assessment of the challenge of predicting the onset of flutter

Computational modelling of dynamic fluid–structure interaction (DFSI) is a considerable challenge. Our approach to this class of problems involves the use of a single software framework for all the phenomena involved, employing finite volume methods on unstructured meshes in three dimensions. This method enables time and space accurate calculations in a consistent manner. One key application of DFSI simulation is the analysis of the onset of flutter in aircraft wings, where the work of Yates et al. [Measured and Calculated Subsonic and Transonic Flutter Characteristics of a 45° degree Sweptback Wing Planform in Air and Freon-12 in the Langley Transonic Dynamic Tunnel. NASA Technical Note D-1616, 1963] on the AGARD 445.6 wing planform still provides the most comprehensive benchmark data available. This paper presents the results of a significant effort to model the onset of flutter for the AGARD 445.6 wing planform geometry. A series of key issues needs to be addressed for this computational approach. • The advantage of using a single mesh, in order to eliminate numerical problems when applying boundary conditions at the fluid-structure interface, is counteracted by the challenge of generating a suitably high quality mesh in both the fluid and structural domains. • The computational effort for this DFSI procedure, in terms of run time and memory requirements, is very significant. Practical simulations require even finer meshes and shorter time steps, requiring parallel implementation for operation on large, high performance parallel systems. • The consistency and completeness of the AGARD data in the public domain is inadequate for use in the validation of DFSI codes when predicting the onset of flutter.

Collaborating components in mesh-based electronic packaging

From the model geometry creation to the model analysis, the stages in between such as mesh generation are the most manpower intensive phase in a mesh-based computational mechanics simulation process. On the other hand the model analysis is the most computing intensive phase. Advanced computational hardware and software have significantly reduced the computing time - and more importantly the trend is downward. With the kind of models envisaged coming, which are larger, more complex in geometry and modelling, and multiphysics, there is no clear trend that the manpower intensive phase is to decrease significantly in time - in the present way of operation it is more likely to increase with model complexity. In this paper we address this dilemma in collaborating components for models in electronic packaging application.

A two dimensional unstructured staggered mesh method with special treatment of tangential velocity

A two dimensional staggered unstructured discretisation scheme for the solution of fluid flow problems has been developed. This scheme stores and solves the velocity vector resolutes normal and parallel to each cell face and other scalar variables (pressure, temperature) are stored at cell centres. The coupled momentum; continuity and energy equations are solved, using the well known pressure correction algorithm SIMPLE. The method is tested for accuracy and convergence behaviour against standard cell-centre solutions in a number of benchmark problems: The Lid-Driven Cavity, Natural Convection in a Cavity and the Melting of Gallium in a rectangular domain.

Unstructured staggered mesh methods for fluid flow, heat transfer and phase change

Unstructured grid meshes used in most commercial CFD codes inevitably adopt collocated variable solution schemes. These schemes have several shortcomings, mainly due to the interpolation of the pressure gradient, that lead to slow convergence. In this publication we show how it is possible to use a much more stable staggered mesh arrangement in an unstructured code. Several alternative groupings of variables are investigated in a search for the optimum scheme.

Numerical simulation of incompressible flow problems using an unstructured staggered mesh method

A number of two dimensional staggered unstructured discretisation schemes for the solution of fluid flow and heat transfer problems have been developed. All schemes store and solve velocity vector components at cell faces with scalar variables solved at cell centres. The velocity is resolved into face-normal and face-parallel components and the various schemes investigated differ in the treatment of the parallel component. Steady-state and time-dependent fluid flow and thermal energy equations are solved with the well known pressure correction scheme, SIMPLE, employed to couple continuity and momentum. The numerical methods developed are tested on well known benchmark cases: the Lid-Driven Cavity, Natural Convection in a Cavity and Melting of Gallium in a rectangular domain. The results obtained are shown to be comparable to benchmark, but with accuracy dependent on scheme selection.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.