7 research outputs found
Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method
Many interfacial phenomena in physical and biological systems are dominated
by high order geometric quantities such as curvature.
Here a semi-implicit method is combined with a level set jet scheme to handle
stiff nonlinear advection problems.
The new method offers an improvement over the semi-implicit gradient
augmented level set method previously introduced by requiring only one
smoothing step when updating the level set jet function while still preserving
the underlying methods higher accuracy. Sample results demonstrate that
accuracy is not sacrificed while strict time step restrictions can be avoided
The Semi Implicit Gradient Augmented Level Set Method
Here a semi-implicit formulation of the gradient augmented level set method
is presented. By tracking both the level set and it's gradient accurate subgrid
information is provided,leading to highly accurate descriptions of a moving
interface. The result is a hybrid Lagrangian-Eulerian method that may be easily
applied in two or three dimensions. The new approach allows for the
investigation of interfaces evolving by mean curvature and by the intrinsic
Laplacian of the curvature. In this work the algorithm, convergence and
accuracy results are presented. Several numerical experiments in both two and
three dimensions demonstrate the stability of the scheme.Comment: 19 Pages, 14 Figure
An Immersed Interface Method for Discrete Surfaces
Fluid-structure systems occur in a range of scientific and engineering
applications. The immersed boundary(IB) method is a widely recognized and
effective modeling paradigm for simulating fluid-structure interaction(FSI) in
such systems, but a difficulty of the IB formulation is that the pressure and
viscous stress are generally discontinuous at the interface. The conventional
IB method regularizes these discontinuities, which typically yields low-order
accuracy at these interfaces. The immersed interface method(IIM) is an IB-like
approach to FSI that sharply imposes stress jump conditions, enabling
higher-order accuracy, but prior applications of the IIM have been largely
restricted to methods that rely on smooth representations of the interface
geometry. This paper introduces an IIM that uses only a C0 representation of
the interface,such as those provided by standard nodal Lagrangian FE methods.
Verification examples for models with prescribed motion demonstrate that the
method sharply resolves stress discontinuities along the IB while avoiding the
need for analytic information of the interface geometry. We demonstrate that
only the lowest-order jump conditions for the pressure and velocity gradient
are required to realize global 2nd-order accuracy. Specifically,we show
2nd-order global convergence rate along with nearly 2nd-order local convergence
in the Eulerian velocity, and between 1st-and 2nd-order global convergence
rates along with 1st-order local convergence for the Eulerian pressure. We also
show 2nd-order local convergence in the interfacial displacement and velocity
along with 1st-order local convergence in the fluid traction. As a
demonstration of the method's ability to tackle complex geometries,this
approach is also used to simulate flow in an anatomical model of the inferior
vena cava.Comment: - Added a non-axisymmetric example (flow within eccentric rotating
cylinder in Sec. 4.3) - Added a more in-depth analysis and comparison with a
body-fitted approach for the application in Sec. 4.