In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.

SUMMARYWe describe the implementation of a computational fluid dynamics solver for the simulation of high-speed flows. It comprises a finite volume (FV) discretization using semi-discrete, non-staggered central schemes for colocated variables prescribed on a mesh of polyhedral cells that have an arbitrary number of faces. We describe the solver in detail, explaining the choice of variables whose face interpolation is limited, the choice of limiter, and a method for limiting the interpolation of a vector field that is independent of the coordinate system. The solution of momentum and energy transport in the Navier-Stokes equations uses an operator-splitting approach: first, we solve an explicit predictor equation for the convection of conserved variables, then an implicit corrector equation for the diffusion of primitive variables. Our solver is validated against four sets of data: (1) an analytical solution of the one-dimensional shock tube case; (2) a numerical solution of two dimensional, transient, supersonic flow over a forward-facing step; (3) interferogram density measurements of a supersonic jet from a circular nozzle; and (4) pressure and heat transfer measurements in hypersonic flow over a 25 • -55 • biconic. Our results indicate that the central-upwind scheme of Kurganov, Noelle and Petrova (SIAM J. Sci. Comput. 2001; 23:707-740) is competitive with the best methods previously published (e.g. piecewise parabolic method, Roe solver with van Leer limiting) and that it is inherently simple and well suited to a colocated, polyhedral FV framework.

SUMMARYA recent emergence of the ÿnite volume method (FVM) in structural analysis promises a viable alternative to the well-established ÿnite element solvers. In this paper, the linear stress analysis problem is discretized using the practices usually associated with the FVM in uid ows. These include the second-order accurate discretization on control volumes of arbitrary polyhedral shape; segregated solution procedure, in which the displacement components are solved consecutively and iterative solvers for the systems of linear algebraic equations. Special attention is given to the optimization of the discretization practice in order to provide rapid convergence for the segregated solution procedure. The solver is set-up to work e ciently on parallel distributed memory computer architectures, allowing a fast turn-around for the mesh sizes expected in an industrial environment. The methodology is validated on two test cases: stress concentration around a circular hole and transient wave propagation in a bar. Finally, the steady and transient stress analysis of a Diesel injector valve seat in 3-D is presented, together with the set of parallel speed-up results.

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The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known total variation diminishing (TVD) and normalised variable diagram (NVD) families of differencing schemes. All of these use some sort of an 'unboundedness indicator' in order to determine the parts of the domain where intervention in the discretisation practice is needed. These, however, all use the 'far upwind' value for each face under consideration, which is not appropriate for unstructured meshes. This paper proposes a modification of the NVD criterion that localises it and thus makes it applicable irrespective of the mesh structure, facilitating the implementation of 'standard' bounded differencing schemes on unstructured meshes. Based on this strategy, a new bounded version of central differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differencing schemes on several model problems.