We present a coupled thermal-fluid model for Bénard-Marangoni convection in a three-dimensional fluid layer. The governing equations are derived in detail for two reasons: first, we do not assume a flat free surface as commonly done; and second, we prepare for the use of flexible discretizations. The governing equations are discretized using spectral elements in space and an operator splitting ...

In this short paper, we introduce an efficient finite element method for solving the Stokes equations based on a divergence free H(div) element. The strong curl of C0-Pk+1 basis functions forms divergence-free subspace Pk-H(div) (i.e. BDMk) space. [Pk+1]2×2 weak gradients are employed these non-H1 to obtain conforming formulation. A strength approach is that saddle point problem replaced by sym...

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Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....

We discuss the stabilized finite element computation of unsteady incompressible flows, with emphasis on the space-time formulations, iterative solution techniques and implementations on the massively parallel architectures such as the Connection Machines. The stabilization technique employed in this paper is the Galerkinjleast-squares (GLS) method. The Deformable-Spatial-DomainjStabilized-Space...

Generalizing from efforts parsing natural language sentences using the grammar formalism, Dependency Grammar (DG) has been emulated by a context-free grammar (CFG) constrained by grammatical function annotation. Single-headedness and projectivity are assumed. This approach has the benefit of making general constraint-based context-free grammar parsing facilities available to DG analysis. This p...

A novel approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay-free controllers in the DT design. In particular, DT controllers can be extracted fro...

A straightforward evaluation approach of free-surface Green function is developed to solve the potential flow around a three-dimensional lifting body. The free-surface waves generated by the movement of the lifting body is presented in an expansion of plane regular waves traveling in θ directions with wave number magnitudes k > 0. A boundary element method is combined with the evaluation approa...