Boundary conditions for incompressible flows
Journal of Scientific Computing
An Object-Oriented Toolbox for Spectral Element Analysis
Journal of Scientific Computing
Role of the LBB condition in weak spectral projection methods: 405
Journal of Computational Physics
SIAM Journal on Scientific Computing
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
A new class of truly consistent splitting schemes for incompressible flows
Journal of Computational Physics
Journal of Scientific Computing
Stokes eigenmodes in cubic domain: primitive variable and Lattice Boltzmann formulations
Applied Numerical Mathematics
Open and traction boundary conditions for the incompressible Navier-Stokes equations
Journal of Computational Physics
Stable and accurate pressure approximation for unsteady incompressible viscous flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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The temporal stability and effective order of two different direct high-order Stokes solvers are examined. Both solvers start from the primitive variables formulation of the Stokes problem, but are distinct by the numerical uncoupling they apply on the Stokes operator. One of these solvers introduces an intermediate divergence free velocity for performing a temporal splitting (J. Comput. Phys. [1991] 97, 414---443) while the other treats the whole Stokes problem through the evaluation of a divergence free acceleration field (C.R. Acad. Sci. Paris [1994] 319 Serie I, 1455---1461; SIAM J. Scient. Comput. [2000] 22(4), 1386---1410). The second uncoupling is known to be consistent with the harmonicity of the pressure field (SIAM J. Scient. Comput. [2000] 22(4), 1386---1410). Both solvers proceed by two steps, a pressure evaluation based on an extrapolated in time (of theoretical order Je) Neumann condition, and a time implicit (of theoretical order Ji) diffusion step for the final velocity. These solvers are implemented with a Chebyshev mono-domain and a Legendre spectral element collocation schemes. The numerical stability of these four options is investigated for the sixteen combinations of (Je,Ji), 1 驴 Je, Ji 驴 4.