3,961 research outputs found
Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae
(Abridged) In the implicit large eddy simulation (ILES) paradigm, the
dissipative nature of high-resolution shock-capturing schemes is exploited to
provide an implicit model of turbulence. Recent 3D simulations suggest that
turbulence might play a crucial role in core-collapse supernova explosions,
however the fidelity with which turbulence is simulated in these studies is
unclear. Especially considering that the accuracy of ILES for the regime of
interest in CCSN, weakly compressible and strongly anisotropic, has not been
systematically assessed before. In this paper we assess the accuracy of ILES
using numerical methods most commonly employed in computational astrophysics by
means of a number of local simulations of driven, weakly compressible,
anisotropic turbulence. We report a detailed analysis of the way in which the
turbulent cascade is influenced by the numerics. Our results suggest that
anisotropy and compressibility in CCSN turbulence have little effect on the
turbulent kinetic energy spectrum and a Kolmogorov scaling is
obtained in the inertial range. We find that, on the one hand, the kinetic
energy dissipation rate at large scales is correctly captured even at
relatively low resolutions, suggesting that very high effective Reynolds number
can be achieved at the largest scales of the simulation. On the other hand, the
dynamics at intermediate scales appears to be completely dominated by the
so-called bottleneck effect, \ie the pile up of kinetic energy close to the
dissipation range due to the partial suppression of the energy cascade by
numerical viscosity. An inertial range is not recovered until the point where
relatively high resolution , which would be difficult to realize in
global simulations, is reached. We discuss the consequences for CCSN
simulations.Comment: 17 pages, 9 figures, matches published versio
High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE)
finite volume scheme on unstructured triangular meshes that is high order
accurate in space and time and that also allows for time-accurate local time
stepping (LTS). The new scheme uses the following basic ingredients: a high
order WENO reconstruction in space on unstructured meshes, an element-local
high-order accurate space-time Galerkin predictor that performs the time
evolution of the reconstructed polynomials within each element, the computation
of numerical ALE fluxes at the moving element interfaces through approximate
Riemann solvers, and a one-step finite volume scheme for the time update which
is directly based on the integral form of the conservation equations in
space-time. The inclusion of the LTS algorithm requires a number of crucial
extensions, such as a proper scheduling criterion for the time update of each
element and for each node; a virtual projection of the elements contained in
the reconstruction stencils of the element that has to perform the WENO
reconstruction; and the proper computation of the fluxes through the space-time
boundary surfaces that will inevitably contain hanging nodes in time due to the
LTS algorithm. We have validated our new unstructured Lagrangian LTS approach
over a wide sample of test cases solving the Euler equations of compressible
gasdynamics in two space dimensions, including shock tube problems, cylindrical
explosion problems, as well as specific tests typically adopted in Lagrangian
calculations, such as the Kidder and the Saltzman problem. When compared to the
traditional global time stepping (GTS) method, the newly proposed LTS algorithm
allows to reduce the number of element updates in a given simulation by a
factor that may depend on the complexity of the dynamics, but which can be as
large as 4.7.Comment: 31 pages, 13 figure
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
Multiple-relaxation-time lattice Boltzmann model for compressible fluids
We present an energy-conserving multiple-relaxation-time finite difference
lattice Boltzmann model for compressible flows. This model is based on a
16-discrete-velocity model. The collision step is first calculated in the
moment space and then mapped back to the velocity space. The moment space and
corresponding transformation matrix are constructed according to the group
representation theory. Equilibria of the nonconserved moments are chosen
according to the need of recovering compressible Navier-Stokes equations
through the Chapman-Enskog expansion. Numerical experiments showed that
compressible flows with strong shocks can be well simulated by the present
model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax,
Sjogreen, Colella explosion wave and collision of two strong shocks, (ii)
regular and Mach shock reflections, and (iii) shock wave reaction on
cylindrical bubble problems. The new model works for both low and high speeds
compressible flows. It contains more physical information and has better
numerical stability and accuracy than its single-relaxation-time version.Comment: 11 figures, Revte
High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows
In this article we present the first better than second order accurate
unstructured Lagrangian-type one-step WENO finite volume scheme for the
solution of hyperbolic partial differential equations with non-conservative
products. The method achieves high order of accuracy in space together with
essentially non-oscillatory behavior using a nonlinear WENO reconstruction
operator on unstructured triangular meshes. High order accuracy in time is
obtained via a local Lagrangian space-time Galerkin predictor method that
evolves the spatial reconstruction polynomials in time within each element. The
final one-step finite volume scheme is derived by integration over a moving
space-time control volume, where the non-conservative products are treated by a
path-conservative approach that defines the jump terms on the element
boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian
(ALE) method, where the mesh velocity can be chosen independently of the fluid
velocity.
The new scheme is applied to the full seven-equation Baer-Nunziato model of
compressible multi-phase flows in two space dimensions. The use of a Lagrangian
approach allows an excellent resolution of the solid contact and the resolution
of jumps in the volume fraction. The high order of accuracy of the scheme in
space and time is confirmed via a numerical convergence study. Finally, the
proposed method is also applied to a reduced version of the compressible
Baer-Nunziato model for the simulation of free surface water waves in moving
domains. In particular, the phenomenon of sloshing is studied in a moving water
tank and comparisons with experimental data are provided
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