The development of the edge implementation is supported by two criteria: the properties of the element based one, which has already been extensively tested and for which convergence and stability analysis has already been presented, and on the enforcement of global conservation and symmetry at the discrete level. A monotonicity preserving term which decreases the discretization order in sharp gradient regions to avoid localized oscillations (overshoots and undershoots), is formulated and tested. Some numerical examples and experimental comparisons are presented

• replacing limiting and approximate Riemann solvers by simpler schemes during the initial stages of Runge–Kutta solvers, and only using limiting and approximate Riemann solvers for the last stage;
• automatically switching to simpler schemes for smooth flow regions;
• automatic deactivation of quiescent regions; and
• unstructured grids with cartesian cores or embedded cartesian grids.

The results from several examples demonstrate that speedup factors of 1:4 are attainable without compromising the accuracy of the traditional FCT schemes.

Two simple mesh operators are used to recursively modify the mesh: edge collapse and point insertion on edge. It is shown that using these operators jointly with a quality function allows to quickly produce an quality anisotropic mesh. Each adaptation entity, ie surface, volume or boundary layers, relies on a specific metric tensor field. The metric-based surface estimate is used to control the deviation to the surface and to adapt the surface mesh. The volume estimate aims at controlling the interpolation error of a specific field of the flow. The boundary layers metric-based estimate is deduced from a level-set distance function.

The aneurysm and parent artery motions in two patients were determined from cine loops of dynamic angiographies. The oscillatory motion amplitude was quantified by registering the frames. Patient‐specific computational fluid dynamics (CFD) models of both aneurysms were constructed from 3D rotational angiography images. Two CFD calculations were performed for each patient, corresponding to static and moving models. The motion estimated from the dynamic images was used to move the surface grid points in the moving model. Visualizations from the simulations were compared for wall shear stress (WSS), velocity profiles, and streamlines.

In both patients, a rigid oscillation of the aneurysm and basilar artery in the anterio‐posterior direction was observed and measured. The distribution of WSS was nearly identical between the models of each patient, as well as major intra‐aneurysmal flow structures, inflow jets, and regions of impingement.

The motion observed in pulsating intracranial vasculature does not have a major impact on intra‐aneurysmal hemodynamic variables. Parent artery motion is unlikely to be a risk factor for increased risk of aneurysmal rupture.

The present Conference was intended to provide a forum to discuss future trends and developments that may affect the way Computational Aerosciences are conducted. One way to venture statements about the future is via exptrapolations from historical trends. In each of the individual disciplines that comprise the aerosciences - aerodynamics, structures, propulsion, control, stealth, etc. - one observes the typical bottom-up trend. Starting from sufficiently simple geometries and equations to have an impact and be identified as `computational’ (e.g., potential flow in 2-D for aerodynamics), more and more realism is added at the geometrical and PDE level. While the engineering process (Figure 1) follows the line: project, objectives, optimization goals, discipline, problem definition, gridding, solution of the PDE and evaluation, the developments in the Computational Sciences tend to run in the opposite direction: solvers, mesh generators, preprocessors, multi-disciplinary links, complete database. At present (1998), for commercial software we are at the threshold mesh generators/ preprocessors, so we can estimate that sometime during the next decade we will see the widespread use of multi-disciplinary links and towards the end of the decade the appearance of integrated analysis and simulation databases. At the research level, we are already entering the complete database approach.

u,t +∇ · (Fa − Fv) = S(u) , (9.1) where u,Fa,Fv,S(u) denote the vector of unknowns, advective and diffusive flux tensors, and source-terms respectively. In the case of compressible gases, we have

u = (ρ ; ρvi ; ρe) ,

Faj = (ρvj ; ρvivj + pδij ; vj(ρe+ p)) ,

Fvj = (0 ; σij ; vlσlj + kT,j) . (9.2)

Here ρ, p, e, T, k, vi denote the density, pressure, specific total energy, temperature, conductivity and fluid velocity in direction xi respectively. This set of equations is closed by providing an equation of state, e.g., for a polytropic gas:

p = (γ − 1)ρ[e− 1 2 vjvj ] , T = cv[e − 1

2 vjvj ] , (9.3 a, b)

where γ, cv are the ratio of specific heats and the specific heat at constant volume respectively. Furthermore, the relationship between the stress tensor σij and the deformation rate must be supplied. For water and almost all gases, Newton’s hypothesis

σij = µ( ∂vi ∂xj

+ ∂vj ∂xi

) + λ ∂vk ∂xk

δij (9.4)

complemented with Stokes’ hypothesis

λ = −2µ 3

(9.5)

is an excellent approximation. The compressible Euler equations are obtained by neglecting the viscous fluxes, i.e., setting Fv = 0. The incompressible Euler or Navier-Stokes equations are obtained by assuming that the density is constant and that pressure does not depend on temperature. The Maxwell equations of electromagnetics, the heat conduction equations of solids, and the equations describing elastic solids undergoing small deformation can readily be written in the form given by Equation (9.1).