4,291 research outputs found
A time dependent Stokes interface problem: well-posedness and space-time finite element discretization
In this paper a time dependent Stokes problem that is motivated by a standard
sharp interface model for the fluid dynamics of two-phase flows is studied.
This Stokes interface problem has discontinuous density and viscosity
coefficients and a pressure solution that is discontinuous across an evolving
interface. This strongly simplified two-phase Stokes equation is considered to
be a good model problem for the development and analysis of finite element
discretization methods for two-phase flow problems. In view of the unfitted
finite element methods that are often used for two-phase flow simulations, we
are particularly interested in a well-posed variational formulation of this
Stokes interface problem in a Euclidean setting. Such well-posed weak
formulations, which are not known in the literature, are the main results of
this paper. Different variants are considered, namely one with suitable spaces
of divergence free functions, a discrete-in-time version of it, and variants in
which the divergence free constraint in the solution space is treated by a
pressure Lagrange multiplier. The discrete-in-time variational formulation
involving the pressure variable for the divergence free constraint is a natural
starting point for a space-time finite element discretization. Such a method is
introduced and results of numerical experiments with this method are presented
Patch-recovery filters for curvature in discontinuous Galerkin-based level-set methods
In two-phase flow simulations, a difficult issue is usually the treatment of
surface tension effects. These cause a pressure jump that is proportional to
the curvature of the interface separating the two fluids. Since the evaluation
of the curvature incorporates second derivatives, it is prone to numerical
instabilities. Within this work, the interface is described by a level-set
method based on a discontinuous Galerkin discretization. In order to stabilize
the evaluation of the curvature, a patch-recovery operation is employed. There
are numerous ways in which this filtering operation can be applied in the whole
process of curvature computation. Therefore, an extensive numerical study is
performed to identify optimal settings for the patch-recovery operations with
respect to computational cost and accuracy.Comment: 25 pages, 8 figures, submitted to Communications in Computational
Physic
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
In this work, we apply stochastic collocation methods with radial kernel
basis functions for an uncertainty quantification of the random incompressible
two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the
existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase
Navier-Stokes equation for each given realization. We are able to empirically
show that the resulting kernel-based stochastic collocation is highly
competitive in this setting and even outperforms some other standard methods
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