1,484 research outputs found
What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives
Intelligent Mesh Generation (IMG) represents a novel and promising field of
research, utilizing machine learning techniques to generate meshes. Despite its
relative infancy, IMG has significantly broadened the adaptability and
practicality of mesh generation techniques, delivering numerous breakthroughs
and unveiling potential future pathways. However, a noticeable void exists in
the contemporary literature concerning comprehensive surveys of IMG methods.
This paper endeavors to fill this gap by providing a systematic and thorough
survey of the current IMG landscape. With a focus on 113 preliminary IMG
methods, we undertake a meticulous analysis from various angles, encompassing
core algorithm techniques and their application scope, agent learning
objectives, data types, targeted challenges, as well as advantages and
limitations. We have curated and categorized the literature, proposing three
unique taxonomies based on key techniques, output mesh unit elements, and
relevant input data types. This paper also underscores several promising future
research directions and challenges in IMG. To augment reader accessibility, a
dedicated IMG project page is available at
\url{https://github.com/xzb030/IMG_Survey}
Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations
A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin (DG), staggered grid, spectral volume (SV), and spectral difference (SD).
The approach is then extended to diffusion equation and Navier-Stokes equations. In the discretization of the diffusion terms, the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches are used. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh.
The current work also includes a study of high-order curve boundaries representations. A new boundary representation based on the Bezier curve is then developed and analyzed, which is shown to have several advantages for complicated geometries.
To further enhance the efficiency, the capability of h/p mesh adaptation is developed for the CPR solver. The adaptation is driven by an efficient multi-p a posteriori error estimator. P-adaptation is applied to smooth regions of the flow field while h-adaptation targets the non-smooth regions, identified by accuracy-preserving TVD marker. Several numerical tests are presented to demonstrate the capability of the technique
Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
Given a tetrahedral mesh and objective functionals measuring the mesh quality
which take into account the shape, size, and orientation of the mesh elements,
our aim is to improve the mesh quality as much as possible. In this paper, we
combine the moving mesh smoothing, based on the integration of an ordinary
differential equation coming from a given functional, with the lazy flip
technique, a reversible edge removal algorithm to modify the mesh connectivity.
Moreover, we utilize radial basis function (RBF) surface reconstruction to
improve tetrahedral meshes with curved boundary surfaces. Numerical tests show
that the combination of these techniques into a mesh improvement framework
achieves results which are comparable and even better than the previously
reported ones.Comment: Revised and improved versio
GPU-accelerated discontinuous Galerkin methods on hybrid meshes
We present a time-explicit discontinuous Galerkin (DG) solver for the
time-domain acoustic wave equation on hybrid meshes containing vertex-mapped
hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable
formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto
(Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions
for hybrid meshes are derived by bounding the spectral radius of the DG
operator using order-dependent constants in trace and Markov inequalities.
Computational efficiency is achieved under a combination of element-specific
kernels (including new quadrature-free operators for the pyramid), multi-rate
timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM
Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows
The present paper addresses the development and implementation of the first
high-order Flux Reconstruction (FR) solver for high-speed flows within the
open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid
Dynamics) platform. The resulting solver is fully implicit and able to simulate
compressible flow problems governed by either the Euler or the Navier-Stokes
equations in two and three dimensions. Furthermore, it can run in parallel on
multiple CPU-cores and is designed to handle unstructured grids consisting of
both straight and curved edged quadrilateral or hexahedral elements. While most
of the implementation relies on state-of-the-art FR algorithms, an improved and
more case-independent shock capturing scheme has been developed in order to
tackle the first viscous hypersonic simulations using the FR method. Extensive
verification of the FR solver has been performed through the use of
reproducible benchmark test cases with flow speeds ranging from subsonic to
hypersonic, up to Mach 17.6. The obtained results have been favorably compared
to those available in literature. Furthermore, so-called super-accuracy is
retrieved for certain cases when solving the Euler equations. The strengths of
the FR solver in terms of computational accuracy per degree of freedom are also
illustrated. Finally, the influence of the characterizing parameters of the FR
method as well as the the influence of the novel shock capturing scheme on the
accuracy of the developed solver is discussed
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