DNS of a plane mixing layer for the investigation of sound generation mechanisms

Babucke, Andreas; Kloker, Markus J.; Rist, Ulrich

doi:10.1016/j.compfluid.2007.02.002

Cited by 34 publications

(33 citation statements)

References 10 publications

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“…In this test, originally proposed in [31] and then extended to three space dimensions in the work of [3] and then reproposed also in [54,37,46], the high order of accuracy of our ADER-DG scheme and the judiciousness of the implementation of the SCL are tested. A well known unsteady physical instability is generated along a compressible two dimensional mixing layer, between the parallel motion of two streams.…”

Section: Compressible 2d Mixing Layermentioning

confidence: 99%

Space–time adaptive ADER-DG schemes for dissipative flows: Compressible Navier–Stokes and resistive MHD equations

Fambri

Dumbser

Zanotti

2017

Computer Physics Communications

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This paper presents an arbitrary high-order accurate ADER Discontinuous Galerkin (DG) method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent partial differential equations for compressible dissipative flows: the compressible Navier-Stokes equations and the equations of viscous and resistive magnetohydrodynamics in two and three space-dimensions.The work continues a recent series of papers concerning the development and application of a proper a posteriori subcell finite volume limiting procedure suitable for discontinuous Galerkin methods [49,112,111]. It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called 'Gibbs phenomenon'. Over the years, several attempts have been made to cope with this problem and different kinds of limiters have been proposed. Among them, a rather intriguing paradigm has been defined in the work of [23], in which the nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a novel a posteriori detection criterion (MOOD approach). In the present work the main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. An important feature of our new scheme is its ability to cure even floating point errors (NaN) that may occur during a simulation, for example when taking real roots of negative numbers or after divisions by zero. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection critera is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Furthermore, in those cells where at least one of these critera is violated the computed candidate solution is detected as troubled and is locally rejected. Next, the numerical solution of the previous time step is scattered onto cell averages of a suitable sub-grid in order to preserve the natural sub-cell resolution of the DG scheme. Subsequently, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume scheme on the subgrid averages within that troubled cell. Finally, a high order DG polynomial is reconstructed back from the evolved subcell averages.We apply the whole approach for the first time to the equations of compressible gas dynamics and magnetohydrodynamics in the presence of viscosity, thermal conductivity and magnetic resistivity, therefore extending our family of adaptive ADER-DG schemes to cases for which the numerical fluxes also depend on the gradient of the state vector.The disting...

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Section: Compressible 2d Mixing Layermentioning

confidence: 99%

Space–time adaptive ADER-DG schemes for dissipative flows: Compressible Navier–Stokes and resistive MHD equations

Fambri

Dumbser

Zanotti

2017

Computer Physics Communications

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“…Fundamentals of the code can be found in [14,23,24]. For details on multicomponent flows, the reader is referred to the textbooks by, e.g., Bird et al [21], Anderson [22], and Hirschfelder et al [25].…”

Section: A Governing Equationsmentioning

confidence: 99%

“…This approach is based on classical compact-finite difference schemes presented in [23,32], which have been optimized to harvest the potential of massively parallel supercomputers by a significantly decreased idling time of the processors. In the spanwise direction, if applicable, the derivatives are computed by means of a Fourier-spectral discretization due to the assumed periodicity of the flowfield.…”

Section: Spatial Discretization and Time Integrationmentioning

confidence: 99%

Influence of Cooling-Gas Properties on Film-Cooling Effectiveness in Supersonic Flow

Keller

Kloker

Olivier

2015

Journal of Spacecraft and Rockets

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Film cooling is considered a prerequisite for the safe operation of future high-performance rocket engines. Wallnormal or inclined cooling-gas injection into a laminar boundary-layer airflow at Mach 2.6 through a single infinite spanwise slit with various cooling gases using direct numerical simulations and experiments are investigated. Among the investigated gases, helium and hydrogen perform best with respect to cooling effectiveness and skin friction decrease. An arbitrary variation of various cooling-gas parameters shows that the diffusion coefficient has virtually no influence on the cooling effectiveness, whereas low cooling-gas viscosity, low thermal conductivity, high heat capacity, low molar mass, and low density are highly beneficial. In light of this large number of parameters, an extension of the single-species cooling-effectiveness correlation to binary gas-mixture flows is challenging, if possible at all. Nomenclature C = Chapman-Rubesin factor c = mass fraction c f = skin friction coefficient c p = heat capacity at constant pressure c v = heat capacity at constant volume D = ordinary diffusion coefficient D T = thermal diffusion coefficient e = internal energy F = blowing rate I = identity matrix j = diffusion mass-flux vector k = Boltzmann constant L = characteristic length M = molar mass Ma = Mach number Pr = Prandtl number p = pressure q = heat-flux vector R = gas constant Re u = unit Reynolds number Re ∞ = global Reynolds number Sc = Schmidt number T = temperature t = time v = velocity vector X = mole fraction x s = slit position x, y, z = streamwise, spanwise, and wall-normal directions α = blowing angle or thermal diffusion rate η = cooling effectiveness ϑ = thermal conductivity κ = specific heat ratio μ = dynamic viscosity ξ = correlation parameter ϵ = second Lennard-Jones parameter ρ = density σ = first Lennard-Jones parameter Ω = transport collision integral Subscripts c = cooling-gas values (species 2) i = species i is = isothermal uc = uncooled w = values at wall ∞ = freestream values (species 1) Superscripts = Eckert values ⋆ = dimensional values

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“…To derive the kinetic energy balance, we multiply the skew-symmetric form of the momentum equation (2) by the velocity v to obtain…”

Section: Kinetic Energy Balancementioning

confidence: 99%

A kinetic energy preserving nodal discontinuous Galerkin spectral element method

Gassner

2014

Numerical Methods in Fluids

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SUMMARYIn this work, we discuss the construction of a skew‐symmetric discontinuous Galerkin (DG) collocation spectral element approximation for the compressible Euler equations. Starting from the skew‐symmetric formulation of Morinishi, we mimic the continuous derivations on a discrete level to find a formulation for the conserved variables. In contrast to finite difference methods, DG formulations naturally have inter‐domain surface flux contributions due to the discontinuous nature of the approximation space. Thus, throughout the derivations we accurately track the influence of the surface fluxes to arrive at a consistent formulation also for the surface terms. The resulting novel skew‐symmetric method differs from the standard DG scheme by additional volume terms. Those volume terms have a special structure and basically represent the discretization error of the different product rules. We use the summation‐by‐parts (SBP) property of the Gauss–Lobatto‐based DG operator and show that the novel formulation is exactly conservative for the mass, momentum, and energy. Finally, an analysis of the kinetic energy balance of the standard DG discretization shows that because of aliasing errors, a nonzero transport source term in the evolution of the discrete kinetic energy mean value may lead to an inconsistent increase or decrease in contrast to the skew‐symmetric formulation. Furthermore, we derive a suitable interface flux that guarantees kinetic energy preservation in combination with the skew‐symmetric DG formulation. As all derivations require only the SBP property of the Gauss–Lobatto‐based DG collocation spectral element method operator and that the mass matrix is diagonal, all results for the surface terms can be directly applied in the context of multi‐domain diagonal norm SBP finite difference methods. Numerical experiments are conducted to demonstrate the theoretical findings. Copyright © 2014 John Wiley & Sons, Ltd.

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DNS of a plane mixing layer for the investigation of sound generation mechanisms

Cited by 34 publications

References 10 publications

Space–time adaptive ADER-DG schemes for dissipative flows: Compressible Navier–Stokes and resistive MHD equations

Space–time adaptive ADER-DG schemes for dissipative flows: Compressible Navier–Stokes and resistive MHD equations

Influence of Cooling-Gas Properties on Film-Cooling Effectiveness in Supersonic Flow

A kinetic energy preserving nodal discontinuous Galerkin spectral element method

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