1,153 research outputs found
A space-time discontinuous Galerkin finite element method for two-fluid problems
A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy.\ud
The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux
On Validating an Astrophysical Simulation Code
We present a case study of validating an astrophysical simulation code. Our
study focuses on validating FLASH, a parallel, adaptive-mesh hydrodynamics code
for studying the compressible, reactive flows found in many astrophysical
environments. We describe the astrophysics problems of interest and the
challenges associated with simulating these problems. We describe methodology
and discuss solutions to difficulties encountered in verification and
validation. We describe verification tests regularly administered to the code,
present the results of new verification tests, and outline a method for testing
general equations of state. We present the results of two validation tests in
which we compared simulations to experimental data. The first is of a
laser-driven shock propagating through a multi-layer target, a configuration
subject to both Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The second
test is a classic Rayleigh-Taylor instability, where a heavy fluid is supported
against the force of gravity by a light fluid. Our simulations of the
multi-layer target experiments showed good agreement with the experimental
results, but our simulations of the Rayleigh-Taylor instability did not agree
well with the experimental results. We discuss our findings and present results
of additional simulations undertaken to further investigate the Rayleigh-Taylor
instability.Comment: 76 pages, 26 figures (3 color), Accepted for publication in the ApJ
Two fluid space-time discontinuous Galerkin finite element method. Part I: numerical algorithm
A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative
Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling
The quality of plastic parts produced through injection molding depends on
many factors. Especially during the filling stage, defects such as weld lines,
burrs, or insufficient filling can occur. Numerical methods need to be employed
to improve product quality by means of predicting and simulating the injection
molding process. In the current work, a highly viscous incompressible
non-isothermal two-phase flow is simulated, which takes place during the cavity
filling. The injected melt exhibits a shear-thinning behavior, which is
described by the Carreau-WLF model. Besides that, a novel discretization method
is used in the context of 4D simplex space-time grids [2]. This method allows
for local temporal refinement in the vicinity of, e.g., the evolving front of
the melt [10]. Utilizing such an adaptive refinement can lead to locally
improved numerical accuracy while maintaining the highest possible
computational efficiency in the remaining of the domain. For demonstration
purposes, a set of 2D and 3D benchmark cases, that involve the filling of
various cavities with a distributor, are presented.Comment: 14 pages, 11 Figures, 4 Table
A Deep Learning Approach for the Computation of Curvature in the Level-Set Method
We propose a deep learning strategy to estimate the mean curvature of
two-dimensional implicit interfaces in the level-set method. Our approach is
based on fitting feed-forward neural networks to synthetic data sets
constructed from circular interfaces immersed in uniform grids of various
resolutions. These multilayer perceptrons process the level-set values from
mesh points next to the free boundary and output the dimensionless curvature at
their closest locations on the interface. Accuracy analyses involving irregular
interfaces, both in uniform and adaptive grids, show that our models are
competitive with traditional numerical schemes in the and norms. In
particular, our neural networks approximate curvature with comparable precision
in coarse resolutions, when the interface features steep curvature regions, and
when the number of iterations to reinitialize the level-set function is small.
Although the conventional numerical approach is more robust than our framework,
our results have unveiled the potential of machine learning for dealing with
computational tasks where the level-set method is known to experience
difficulties. We also establish that an application-dependent map of local
resolutions to neural models can be devised to estimate mean curvature more
effectively than a universal neural network.Comment: Submitted to SIAM Journal on Scientific Computin
Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method
10.1016/j.jcp.2007.12.002Journal of Computational Physics22763358-3382JCTP
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