A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application.

A new general cell-centered solution procedure based upon the conventional control or finite volume (CV or FV) approach has been developed for numerical heat transfer and fluid flow which encompasses both structured and unstructured meshes for any kind of mixed polygon cell. Unlike conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, the irregular control volume (ICV) method does not require the shape of the element or cell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mixtures of triangular, quadrilateral, and any other higher order polygonal cells to be exploited using a single solution procedure. The ICV approach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, collocation of variables at cell centers is used with a Rhie and Chow interpolation (to suppress pressure oscillation in the flow field) in the context of the SIMPLE pressure correction solution procedure. In fact all other FV structured mesh-based methods may be perceived as a subset of the ICV formulation. The new ICV formulation is benchmarked using two standard computational fluid dynamics (CFD) problems i.e., the moving lid cavity and the natural convection driven cavity. Both cases were solved with a variety of structured and unstructured meshes, the latter exploiting mixed polygonal cell meshes. The polygonal mesh experiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these results may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with changing direction.

Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.

Numerical modelling and validation of Marangoni and surface tension phenomena using the finite volume method

Surface tension induced flow is implemented into a numerical modelling framework and validated for a number of test cases. Finite volume unstructured mesh techniques are used to discretize the mass, momentum and energy conservation equations in three dimensions. An explicit approach is used to include the effect of surface tension forces on the flow profile and final shape of a liquid domain. Validation of this approach is made against both analytical and experimental data. Finally, the method is used to model the wetting balance test for solder alloy material, where model predictions are used to gain a greater insight into this process. Copyright © 2000 John Wiley & Sons, Ltd.

Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

Finite volume methods applied to the computational modelling of welding phenomena

This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of computational fluid dynamics (CFD) and computational solid mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred finite volume (FV) methods are employed. Additionally, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Predictions of segregation of granular material with the aid of PHYSICA, a 3-D unstructured finite-volume modelling framework

In this paper a continuum model for the prediction of segregation in granular material is presented. The numerical framework, a 3-D, unstructured grid, finite-volume code is described, and the micro-physical parametrizations, which are used to describe the processes and interactions at the microscopic level that lead to segregation, are analysed. Numerical simulations and comparisons with experimental data are then presented and conclusions are drawn on the capability of the model to accurately simulate the behaviour of granular matter during flow.

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 approach to geometrically non-linear stress analysis

In this past decade finite volume (FV) methods have increasingly been used for the solution of solid mechanics problems. This contribution describes a cell vertex finite volume discretisation approach to the solution of geometrically nonlinear (GNL) problems. These problems, which may well have linear material properties, are subject to large deformation. This requires a distinct formulation, which is described in this paper together with the solution strategy for GNL problem. The competitive performance for this procedure against the conventional finite element (FE) formulation is illustrated for a three dimensional axially loaded column.

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.

Dynamic solid mechanics using finite volume methods

A procedure for evaluating the dynamic structural response of elastic solid domains is presented. A prerequisite for the analysis of dynamic fluid–structure interaction is the use of a consistent set of finite volume (FV) methods on a single unstructured mesh. This paper describes a three-dimensional (3D) FV, vertex-based method for dynamic solid mechanics. A novel Newmark predictor–corrector implicit scheme was developed to provide time accurate solutions and the scheme was evaluated on a 3D cantilever problem. By employing a small amount of viscous damping, very accurate predictions of the fundamental natural frequency were obtained with respect to both the amplitude and period of oscillation. This scheme has been implemented into the multi-physics modelling software framework, PHYSICA, for later application to full dynamic fluid structure interaction.