Gérard Labrosse

High-Order Direct Stokes Solvers with or Without Temporal Splitting: Numerical Investigations of Their Comparative Properties

A recently proposed direct Stokes solver which decouples the velocity and pressure operators without calling for a temporal scheme is numerically analyzed, in comparison, first with the splitting scheme proposed by G. Karniadakis, M. Israeli, and S. Orszag in [ J. Comput. Phys., 97 (1991), pp. 414--443], and with the unique grid (

STABILITY OF THE AXISYMMETRIC BUOYANT-CAPILLARY FLOWS IN A LATERALLY HEATED LIQUID BRIDGE

{\Bbb{P}}_{N}, {\Bbb{P}}_{N-2}

Soret-driven thermosolutal convection in a vertical enclosure

) Uzawa approach for the space accuracy and computational costs. The Chebyshev collocation approximation is used to analyze the spectra of the continuous temporal evolution operators, and their discrete time versions, from the first to the fourth order. An explicit boundary condition is also involved in the proposed Stokes solver, and it is numerically shown that the trace of

Numerical Evaluation of the Accuracy and Stability Properties of High-order Direct Stokes Solvers with or without Temporal Splitting

{\bf \Delta }{ \bf u}

Up to the unsteadiness of axisymmetric thermocapillary flows in a laterally heated liquid bridge

on the boundary must be evaluated through its

On the numerical treatment of viscous singularities in wall-confined thermocapillary convection

-{\bf \nabla} \times {\bf \nabla} \times

Sensitivity of the liquid bridge hydrodynamics to local capillary contributions

contribution only; otherwise the ellipticity is lost before proceeding to the time discretization. The explicit evaluation of the rotational boundary term does not prevent the first and second order in time schemes from being unconditionally stable, while the schemes built at the next two higher orders are limited by the usual explicit (

A spectral anelastic Navier-Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel

{\cal {O}}(N^{-4})

The piecewise-linear Finite Volume scheme: The best known lowest-order preconditioner for the d2dx2 Chebyshev spectral operator

) stability criterion on the time step. The proposed

Sensitivity of binary liquid thermal convection to confinement

({\bf u},p)