1,641 research outputs found
Stable, entropy-consistent, and localized artificial-diffusivity method for capturing discontinuities
In this work, a localized artificial-viscosity/diffusivity method is proposed
for accurately capturing discontinuities in compressible flows. There have been
numerous efforts to improve the artificial diffusivity formulation in the last
two decades, through appropriate localization of the artificial bulk viscosity
for capturing shocks. However, for capturing contact discontinuities, either a
density or internal energy variable is used as a detector. An issue with this
sensor is that it not only detects contact discontinuities, but also falsely
detects the regions of shocks and vortical motions. Using this detector to add
artificial mass/thermal diffusivity for capturing contact discontinuities is
hence unnecessarily dissipative. To overcome this issue, we propose a sensor
similar to the Ducros sensor (for shocks) to detect contact discontinuities,
and further localize artificial mass/thermal diffusivity for capturing contact
discontinuities.
The proposed method contains coefficients that are less sensitive to the
choice of the flow problem. This is achieved by improved localization of the
artificial diffusivity in the present method. A discretely consistent
dissipative flux formulation is presented and is coupled with a robust
low-dissipative scheme, which eliminates the need for filtering the solution
variables. The proposed method also does not require filtering for the
discontinuity detector/sensor functions, which is typically done to smear out
the artificial fluid properties and obtain stable solutions. Hence, the
challenges associated with extending the filtering procedure for unstructured
grids is eliminated, thereby, making the proposed method easily applicable for
unstructured grids. Finally, a straightforward extension of the proposed method
to two-phase flows is also presented.Comment: 24 pages, 11 figures, Under review in the Physical Review Fluids
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Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws
A novel hybrid spectral difference/embedded finite volume method is
introduced in order to apply a discontinuous high-order method for large scale
engineering applications involving discontinuities in the flows with complex
geometries. In the proposed hybrid approach, the finite volume (FV) element,
consisting of structured FV subcells, is embedded in the base hexahedral
element containing discontinuity, and an FV based high-order shock-capturing
scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is
captured at the resolution of FV subcells within an embedded FV element. In the
smooth flow region, the SD element is used in the base hexahedral element.
Then, the governing equations are solved by the SD method. The SD method is
chosen for its low numerical dissipation and computational efficiency
preserving high-order accurate solutions. The coupling between the SD element
and the FV element is achieved by the globally conserved mortar method. In this
paper, the 5th-order WENO scheme with the characteristic decomposition is
employed as the shock-capturing scheme in the embedded FV element, and the
5th-order SD method is used in the smooth flow field.
The order of accuracy study and various 1D and 2D test cases are carried out,
which involve the discontinuities and vortex flows. Overall, it is shown that
the proposed hybrid method results in comparable or better simulation results
compared with the standalone WENO scheme when the same number of solution DOF
is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the
Journal of Computational Physics, April 201
Inverse asymptotic treatment: capturing discontinuities in fluid flows via equation modification
A major challenge in developing accurate and robust numerical solutions to
multi-physics problems is to correctly model evolving discontinuities in field
quantities, which manifest themselves as interfaces between different phases in
multi-phase flows, or as shock and contact discontinuities in compressible
flows. When a quick response is required to rapidly emerging challenges, the
complexity of bespoke discretization schemes impedes a swift transition from
problem formulation to computation, which is exacerbated by the need to compose
multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT)
as a unified framework for capturing discontinuities in fluid flows that
enables building directly computable models based on off-the-shelf numerics. By
capturing discontinuities through modifications at the level of the governing
equations, IAT can seamlessly handle additional physics and thus enable novice
end users to quickly obtain numerical results for various multi-physics
scenarios. We outline IAT in the context of phase-field modeling of two-phase
incompressible flows, and then demonstrate its generality by showing how
localized artificial diffusivity (LAD) methods for single-phase compressible
flows can be viewed as instances of IAT. Through the real-world example of a
laminar hypersonic compression corner, we illustrate IAT's ability to, within
just a few months, generate a directly computable model whose wall metrics
predictions for sufficiently small corner angles come close to that of NASA's
VULKAN-CFD solver. Finally, we propose a novel LAD approach via
"reverse-engineered" PDE modifications, inspired by total variation diminishing
(TVD) flux limiters, to eliminate the problem-dependent parameter tuning that
plagues traditional LAD. We demonstrate that, when combined with second-order
central differencing, it can robustly and accurately model compressible flows
Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling
© Copyright [2015] American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (https://www.ametsoc.org/) or from the AMS at 617-227-2425 or [email protected] oscillation can show up near flow regions with strong temperature gradients in the numerical simulation of nonhydrostatic mesoscale atmospheric flows when using the high-order discontinuous Galerkin (DG) method. The authors propose to incorporate flow-feature-based localized Laplacian artificial viscosity in the DG framework to suppress the spurious oscillation in the vicinity of sharp thermal fronts but not to contaminate the smooth flow features elsewhere. The parameters in the localized Laplacian artificial viscosity are modeled based on both physical criteria and numerical features of the DG discretization. The resulting numerical formulation is first validated on several shock-involved test cases, including a shock discontinuity problem with the one-dimensional Burger’s equation, shock–entropy wave interaction, and shock–vortex interaction. Then the efficacy of the developed numerical formulation on stabilizing thermal fronts in nonhydrostatic mesoscale atmospheric modeling is demonstrated by two benchmark test cases: the rising thermal bubble problem and the density current problem. The results indicate that the proposed flow-feature-based localized Laplacian artificial viscosity method can sharply detect the nonsmooth flow features, and stabilize the DG discretization nearby. Furthermore, the numerical stabilization method works robustly for a wide range of grid sizes and polynomial orders without parameter tuning in the localized Laplacian artificial viscosity
A New Family of Discontinuous Galerkin Schemes for Diffusion Problems
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143057/1/6.2017-3444.pd
High-Order Methods for Computational Fluid Dynamics: A Brief Review of Compact Differential Formulations on Unstructured Grids
Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent developments for the FR/CPR schemes as well as some pacing items
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