2,807 research outputs found
Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes
In the previous studies, the high-order gas-kinetic schemes (HGKS) have
achieved successes for unsteady flows on three-dimensional unstructured meshes.
In this paper, to accelerate the rate of convergence for steady flows, the
implicit non-compact and compact HGKSs are developed. For non-compact scheme,
the simple weighted essentially non-oscillatory (WENO) reconstruction is used
to achieve the spatial accuracy, where the stencils for reconstruction contain
two levels of neighboring cells. Incorporate with the nonlinear generalized
minimal residual (GMRES) method, the implicit non-compact HGKS is developed. In
order to improve the resolution and parallelism of non-compact HGKS, the
implicit compact HGKS is developed with Hermite WENO (HWENO) reconstruction, in
which the reconstruction stencils only contain one level of neighboring cells.
The cell averaged conservative variable is also updated with GMRES method.
Simultaneously, a simple strategy is used to update the cell averaged gradient
by the time evolution of spatial-temporal coupled gas distribution function. To
accelerate the computation, the implicit non-compact and compact HGKSs are
implemented with the graphics processing unit (GPU) using compute unified
device architecture (CUDA). A variety of numerical examples, from the subsonic
to supersonic flows, are presented to validate the accuracy, robustness and
efficiency of both inviscid and viscous flows.Comment: arXiv admin note: text overlap with arXiv:2203.0904
Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows
The aim of the present paper is to provide a comparison between several
finite-volume methods of different numerical accuracy: second-order Godunov
method with PPM interpolation and high-order finite-volume WENO method. The
results show that while on a smooth problem the high-order method perform
better than the second-order one, when the solution contains a shock all the
methods collapse to first-order accuracy. In the context of the decay of
compressible homogeneous isotropic turbulence with shocklets, the actual
overall order of accuracy of the methods reduces to second-order, despite the
use of fifth-order reconstruction schemes at cell interfaces. Most important,
results in terms of turbulent spectra are similar regardless of the numerical
methods employed, except that the PPM method fails to provide an accurate
representation in the high-frequency range of the spectra. It is found that
this specific issue comes from the slope-limiting procedure and a novel hybrid
PPM/WENO method is developed that has the ability to capture the turbulent
spectra with the accuracy of a high-order method, but at the cost of the
second-order Godunov method. Overall, it is shown that virtually the same
physical solution can be obtained much faster by refining a simulation with the
second-order method and carefully chosen numerical procedures, rather than
running a coarse high-order simulation. Our results demonstrate the importance
of evaluating the accuracy of a numerical method in terms of its actual
spectral dissipation and dispersion properties on mixed smooth/shock cases,
rather than by the theoretical formal order of convergence rate.Comment: This paper was previously composed of 2 parts, and this submission
was part 1. It is now replaced by the combined pape
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA
High-order gas-kinetic scheme with TENO class reconstruction for the Euler and Navier-Stokes equations
The high-order gas-kinetic scheme(HGKS) with WENO spatial reconstruction
method has been extensively validated through many numerical experiments,
demonstrating its superior accuracy efficiency, and robustness. Compared with
WENO class schemes, TENO class schemes exhibit significantly improved
robustness, low numerical dissipation and sharp discontinuity capturing. In
this paper, two kinds of fifth-order HGKS with TENO class schemes are designed.
One involves replacing WENO5 scheme with the TENO5 scheme in the conventional
WENO5-GKS. WENO and TENO schemes only provide the non-equilibrium state values
at the cell interface. The slopes of the non-equilibrium state along with the
equilibrium values and slopes, are obtained by additional linear
reconstruction. Another kind of TENO5-D GKS is similar to WENO5-AO GKS.
Following a strong scale-separation procedure, a tailored novel ENO-like
stencil selection strategy is proposed such that the high-order accuracy is
restored in smooth regions by selecting the candidate reconstruction on the
large stencil while the ENO property is enforced near discontinuities by
adopting the candidate reconstruction from smooth small stencils. The such TENO
schemes are TENO-AA and TENO-D scheme. The HGKS scheme based on WENO-AO or
TENO-D reconstruction take advantage of the large stencil to provide point
values and slopes of the non-equilibrium state. By dynamically merging the
reconstructed non-equilibrium slopes, extra reconstruction of the equilibrium
state at the beginning of each time step can be avoided. The simplified schemes
have better robustness and efficiency than the conventional WENO5-GKS or
TENO5-GKS. TENO-D GKS is also as easy to develop as WENO-AO GKS to high-order
finite volume method for unstructured mesh.Comment: arXiv admin note: text overlap with arXiv:2304.05572; text overlap
with arXiv:1905.08489 by other author
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