Abstract

In this paper, we introduce a way to approximate the subscales on the boundaries of the elements in a variational two-scale finite element approximation to flow problems. The key idea is that the subscales on the element boundaries must be such that the transmission conditions for the unknown, split as its finite element contribution and the subscale, hold. In particular, we consider the scalar convection–diffusion–reaction equation, the Stokes problem and Darcy’s problem. For these problems the transmission conditions are the continuity of the unknown and its fluxes through element boundaries. The former is automatically achieved by introducing a single valued subscale on the boundaries (for the conforming approximations we consider), whereas the latter provides the effective condition for approximating these values. The final result is that the subscale on the interelement boundaries must be proportional to the jump of the flux of the finite element component and the average of the subscale calculated in the element interiors.

Abstract

In this article, we analyze some residual-based stabilization techniques for the transient Stokes problem when considering anisotropic time–space discretizations. We define an anisotropic time–space discretization as a family of time–space partitions that does not satisfy the condition h2⩽Cδt with C uniform with respect to h and δt. Standard residual-based stabilization techniques are motivated by a multiscale approach, approximating the effect of the subscales onto the large scales. One of the approximations is to consider the subscales quasi-static (neglecting their time derivative). It is well known that these techniques are unstable for anisotropic time–space discretizations. We show that the use of dynamic subscales (where the subscales time derivatives are not neglected) solves the problem, and prove optimal convergence and stability results that are valid for anisotropic time–space discretizations. Also the improvements related to the use of orthogonal subscales are addressed.

Abstract

The need for an increase of production rate in aerospace industry implies a growing interest in composite manufacturing process simulation with a strong requirement on predictive accuracy. In this context, ESI enhanced its PAM-COMPOSITES software introducing fluid-solid coupled approach in PAM-RTM module in order to simulate more accurately Vacuum Assisted Resin Infusion (VARI) process.

VARI consists in impregnating a dry preform laid on a rigid mold and placed under a distribution medium and a vacuum bag. During the impregnation resin flows preferentially into the distribution medium and then in the preform which may undergo deformations due to the flexibility of the vacuum bag.

Usual 2.5D approaches, using shell elements with thickness depending on resin pressure, cannot account for resin flow through the thickness due to permeability and fiber fraction gradients implied by the material used and/or solid mechanics effects (such as compression in curvatures).

ESI new approach, resulting from several years of collaboration with academics, consists in a 3D finite element modeling. It is based on the coupling of resin flow, governed by Darcy’s law, with the preform behavior, considered as porous medium undergoing deformations, through Terzaghi’s principle. Thus it results in more predictive filling time and properties (thicknesses, fiber volume contents, geometry) of the final product.