1,781 research outputs found
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
Compact-Reconstruction Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
A new class of non-linear compact interpolation schemes is introduced in this dissertation that have a high spectral resolution and are non-oscillatory across discontinuities. The Compact-Reconstruction Weighted Essentially Non-Oscillatory (CRWENO) schemes use a solution-dependent combination of lower-order compact schemes to yield a high-order accurate, non-oscillatory scheme. Fifth-order accurate CRWENO schemes are constructed and their numerical properties are analyzed. These schemes have lower absolute errors and higher spectral resolution than the WENO scheme of the same order.
The schemes are applied to scalar conservation laws and the Euler equations of fluid dynamics. The order of convergence and the higher accuracy of the CRWENO schemes are verified for smooth solutions. Significant improvements are observed in the resolution of discontinuities and extrema as well as the preservation of flow features over large convection distances. The computational cost of the CRWENO schemes is assessed and the reduced error in the solution outweighs the additional expense of the implicit scheme, thus resulting in higher numerical efficiency. This conclusion extends to the reconstruction of conserved and primitive variables for the Euler equations, but not to the characteristic-based reconstruction. Further improvements are observed in the accuracy and resolution of the schemes with alternative formulations for the non-linear weights.
The CRWENO schemes are integrated into a structured, finite-volume Navier-Stokes solver and applied to problems of practical relevance. Steady and unsteady flows around airfoils are solved to validate the scheme for curvi-linear grids, as well as overset grids with relative motion. The steady flow around a three-dimensional wing and the unsteady flow around a full-scale rotor are solved. It is observed that though lower-order schemes suffice for the accurate prediction of aerodynamic forces, the CRWENO scheme yields improved resolution of near-blade and wake flow features, including boundary and shear layers, and shed vortices. The high spectral resolution, coupled with the non-oscillatory behavior, indicate their suitability for the direct numerical simulation of compressible turbulent flows. Canonical flow problems -- the decay of isotropic turbulence and the shock-turbulence interaction -- are solved. The CRWENO schemes show an improved resolution of the higher wavenumbers and the small-length-scale flow features that are characteristic of turbulent flows.
Overall, the CRWENO schemes show significant improvements in resolving and preserving flow features over a large range of length scales due to the higher spectral resolution and lower dissipation and dispersion errors, compared to the WENO schemes. Thus, these schemes are a viable alternative for the numerical simulation of compressible, turbulent flows
Low-Dissipation Advection Schemes Designed for Large Eddy Simulations of Hypersonic Propulsion Systems
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity
THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
We present THC: a new high-order flux-vector-splitting code for Newtonian and
special-relativistic hydrodynamics designed for direct numerical simulations of
turbulent flows. Our code implements a variety of different reconstruction
algorithms, such as the popular weighted essentially non oscillatory and
monotonicity-preserving schemes, or the more specialised bandwidth-optimised
WENO scheme that has been specifically designed for the study of compressible
turbulence. We show the first systematic comparison of these schemes in
Newtonian physics as well as for special-relativistic flows. In particular we
will present the results obtained in simulations of grid-aligned and oblique
shock waves and nonlinear, large-amplitude, smooth adiabatic waves. We will
also discuss the results obtained in classical benchmarks such as the
double-Mach shock reflection test in Newtonian physics or the linear and
nonlinear development of the relativistic Kelvin-Helmholtz instability in two
and three dimensions. Finally, we study the turbulent flow induced by the
Kelvin-Helmholtz instability and we show that our code is able to obtain
well-converged velocity spectra, from which we benchmark the effective
resolution of the different schemes.Comment: Updated to match the published versio
Implicit large eddy simulation for unsteady multi-component compressible turbulent flows
Numerical methods for the simulation of shock-induced turbulent mixing have been
investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent
mixing is of particular importance for many astrophysical phenomena, inertial confinement
fusion, and mixing in supersonic combustion. These disciplines are particularly
reliant on numerical simulation, as the extreme nature of the flow in question makes
gathering accurate experimental data difficult or impossible.
A detailed quantitative study of homogeneous decaying turbulence demonstrates that
existing state of the art methods represent the growth of turbulent structures and the decay
of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation
is that the numerical methods are too dissipative at high wavenumbers (short
wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of
kinetic energy in low Mach number flows shows that the leading order dissipation rate
for Godunov-type schemes is proportional to the speed of sound and the velocity jump
across the cell interface squared. This shows that the dissipation of Godunov-type
schemes becomes large for low Mach flow features, hence impeding the development
of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra.
It is shown that this leading order term can be removed by locally modifying the reconstruction
of the velocity components. As the modification is local, it allows the
accurate simulation of mixed compressible/incompressible flows without changing the
formulation of the governing equations. In principle, the modification is applicable to
any finite volume compressible method which includes a reconstruction stage. Extensive
numerical tests show great improvements in performance at low Mach compared
to the standard scheme, significantly improving turbulent kinetic energy spectra, and
giving the correct Mach squared scaling of pressure and density variations down to
Mach 10−4. The proposed modification does not significantly affect the shock capturing
ability of the numerical scheme.
The modified numerical method is validated through simulations of compressible,
deep, open cavity flow where excellent results are gained with minimal modelling
effort. Simulations of single and multimode Richtmyer-Meshkov instability show that
the modification gives equivalent results to the standard scheme at twice the grid resolution
in each direction. This is equivalent to sixteen times decrease in computational
time for a given quality of results. Finally, simulations of a shock-induced turbulent
mixing experiment show excellent qualitative agreement with available experimental
data
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