600 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
journa
A physics-based shock capturing method for unsteady laminar and turbulent flows
We present a shock capturing method for unsteady laminar and turbulent flows. The proposed approach relies on physical principles to increase selected transport coefficients and resolve unstable sharp features, such as shock waves and strong thermal and shear gradients, over the smallest distance allowed by the discretization. In particular, we devise various sensors to detect when the shear viscosity, bulk viscosity and thermal conductivity of the fluid do not suffice to stabilize the numerical solution. In such cases, the transport coefficients are increased as necessary to optimally resolve these features with the available resolution. The performance of the method is illustrated through numerical simulation of external and internal flows in transonic, supersonic, and hypersonic regimes.United States. Air Force. Office of Scientific Research (FA9550-16-1-0214)Pratt & Whitney Aircraft CompanyFundación Obra Social de La CaixaMassachusetts Institute of Technology. Office of the Dean for Graduate Education (Zakhartchenko Fellowship
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
Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results
Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations
High-speed turbulent flows are encountered in most space-related applications
(including exploration, tourism and defense fields) and represent a subject of
growing interest in the last decades. A major challenge in performing
high-fidelity simulations of such flows resides in the stringent requirements
for the numerical schemes to be used. These must be robust enough to handle
strong, unsteady discontinuities, while ensuring low amounts of intrinsic
dissipation in smooth flow regions. Furthermore, the wide range of temporal and
spatial active scales leads to concurrent needs for numerical stabilization and
accurate representation of the smallest resolved flow scales in cases of
under-resolved configurations. In this paper, we present a finite-difference
high-order shock-capturing technique based on Jameson's artificial diffusivity
methodology. The resulting scheme is ninth-order-accurate far from
discontinuities and relies on the addition of artificial dissipation close to
large gradients. The shock detector is slightly revised to enhance its
selectivity and avoid spurious activations of the shock-capturing term. A suite
of test cases ranging from 1D to 3D configurations (namely, shock tubes,
Shu-Osher problem, isentropic vortex advection, under-expanded jet,
compressible Taylor-Green Vortex, supersonic and hypersonic turbulent boundary
layers) is analysed in order to test the capability of the proposed numerical
strategy to handle a large variety of problems, ranging from
calorically-perfect air to multi-species reactive flows. Results obtained on
under-resolved grids are also considered to test the applicability of the
proposed strategy in the context of implicit Large-Eddy Simulations
- …