4,514 research outputs found
GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
We present two new Lagrangian methods for hydrodynamics, in a systematic
comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The
new methods are designed to simultaneously capture advantages of both
smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement
(AMR) schemes. They are based on a kernel discretization of the volume coupled
to a high-order matrix gradient estimator and a Riemann solver acting over the
volume 'overlap.' We implement and test a parallel, second-order version of the
method with self-gravity & cosmological integration, in the code GIZMO: this
maintains exact mass, energy and momentum conservation; exhibits superior
angular momentum conservation compared to all other methods we study; does not
require 'artificial diffusion' terms; and allows the fluid elements to move
with the flow so resolution is automatically adaptive. We consider a large
suite of test problems, and find that on all problems the new methods appear
competitive with moving-mesh schemes, with some advantages (particularly in
angular momentum conservation), at the cost of enhanced noise. The new methods
have many advantages vs. SPH: proper convergence, good capturing of
fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical
viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing.
Advantages vs. non-moving meshes include: automatic adaptivity, dramatically
reduced advection errors & numerical overmixing, velocity-independent errors,
accurate coupling to gravity, good angular momentum conservation and
elimination of 'grid alignment' effects. We can, for example, follow hundreds
of orbits of gaseous disks, while AMR and SPH methods break down in a few
orbits. However, fixed meshes minimize 'grid noise.' These differences are
important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code,
user's guide, test problem setups, and movies are available at
http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm
"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
We present a new 3D general relativistic hydrodynamics code for simulations
of stellar core collapse to a neutron star, as well as pulsations and
instabilities of rotating relativistic stars. It uses spectral methods for
solving the metric equations, assuming the conformal flatness approximation for
the three-metric. The matter equations are solved by high-resolution
shock-capturing schemes. We demonstrate that the combination of a finite
difference grid and a spectral grid can be successfully accomplished. This
"Mariage des Maillages" (French for grid wedding) approach results in high
accuracy of the metric solver and allows for fully 3D applications using
computationally affordable resources, and ensures long term numerical stability
of the evolution. We compare our new approach to two other, finite difference
based, methods to solve the metric equations. A variety of tests in 2D and 3D
is presented, involving highly perturbed neutron star spacetimes and
(axisymmetric) stellar core collapse, demonstrating the ability to handle
spacetimes with and without symmetries in strong gravity. These tests are also
employed to assess gravitational waveform extraction, which is based on the
quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests
and grid setu
An Overview of Variational Integrators
The purpose of this paper is to survey some recent advances in variational
integrators for both finite dimensional mechanical systems as well as continuum
mechanics. These advances include the general development of discrete
mechanics, applications to dissipative systems, collisions, spacetime integration algorithms,
AVI’s (Asynchronous Variational Integrators), as well as reduction for
discrete mechanical systems. To keep the article within the set limits, we will only
treat each topic briefly and will not attempt to develop any particular topic in
any depth. We hope, nonetheless, that this paper serves as a useful guide to the
literature as well as to future directions and open problems in the subject
Multidimensional adaptive order GP-WENO via kernel-based reconstruction
This paper presents a fully multidimensional kernel-based reconstruction
scheme for finite volume methods applied to systems of hyperbolic conservation
laws, with a particular emphasis on the compressible Euler equations.
Non-oscillatory reconstruction is achieved through an adaptive order weighted
essentially non-oscillatory (WENO-AO) method cast into a form suited to
multidimensional stencils and reconstruction. A kernel-based approach inspired
by Gaussian process (GP) modeling is presented here. This approach allows the
creation of a scheme of arbitrary order with simply defined multidimensional
stencils and substencils. Furthermore, the fully multidimensional nature of the
reconstruction allows a more straightforward extension to higher spatial
dimensions and removes the need for complicated boundary conditions on
intermediate quantities in modified dimension-by-dimension methods. In
addition, a new simple-yet-effective set of reconstruction variables is
introduced, as well as an easy-to-implement effective limiter for positivity
preservation, both of which could be useful in existing schemes with little
modification. The proposed scheme is applied to a suite of stringent and
informative benchmark problems to demonstrate its efficacy and utility.Comment: Submitted to Journal of Computational Physics April 202
Vorticity capturing
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76188/1/AIAA-2001-2523-514.pd
An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing
The second paper of this series presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element(DGSEM)discretizations of the compressible magneto-hydrodynamics (MHD) equations. Specifically, we use the resistive GLM-MHD equations, which include a divergence cleaning mechanism that is based on a generalized Lagrange multiplier (GLM). For the continuous entropy analysis to hold, and due to the divergence-free constraint on the magnetic field, the GLM-MHD system requires the use of non-conservative terms, which need special treatment.
Hennemann et al. ["A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations". JCP, 2020] recently presented an entropy stable shock-capturing strategy for DGSEM discretizations of the Euler equations that blends the DGSEM scheme with a subcell first-order finite volume (FV) method. Our first contribution is the extension of the method of Hennemann et al. to systems with non-conservative terms, such as the GLM-MHD equations. In our approach, the advective and non-conservative terms of the equations are discretized with a hybrid FV/DGSEM scheme, whereas the visco-resistive terms are discretized only with the high-order DGSEM method. We prove that the extended method is entropy stable on three-dimensional unstructured curvilinear meshes. Our second contribution is the derivation and analysis of a second entropy stable shock-capturing method that provides enhanced resolution by using a subcell reconstruction procedure that is carefully built to ensure entropy stability.
We provide a numerical verification of the properties of the hybrid FV/DGSEM schemes on curvilinear meshes and show their robustness and accuracy with common benchmark cases, such as the Orszag-Tang vortex and the GEM (Geospace Environmental Modeling) reconnection challenge. Finally, we simulate a space physics application: the interaction of Jupiter's magnetic field with the plasma torus generated by the moon Io
- …