Application of approximate dispersion-diffusion analyses to under-resolved Burgers turbulence using high resolution WENO and UWC schemes

Solán-Fustero, P.; Navas-Montilla, Adrián; Ferrer, Esteban; Manzanero, Juan; García‐Navarro, P.

doi:10.1016/j.jcp.2021.110246

Cited by 11 publications

(2 citation statements)

References 46 publications

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“…DG methods have dissipation and dispersive errors, which are confined to high wavenumbers, and therefore introduce numerical dissipation primarily to under-resolved wave-lengths [84]. This property makes them very suitable for ILES, since dissipation only acts at under-resolved scales, as explained in [29,85,86,87]. Riemman solvers are the classic option to include numerical dissipation in DG schemes [1,35], since they naturally arise when discretising the non-linear terms.…”

Section: Turbulence Closure Modelsmentioning

confidence: 99%

HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

Ferrer¹,

Rubio²,

Ntoukas³

et al. 2022

Preprint

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We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics. We provide an overview of the high-order spatial discretisation (including energy/entropy stable schemes) and anisotropic p-adaptation capabilities. The solver is parallelised using MPI and OpenMP showing good scalability for up to 1000 processors. Temporal discretisations include explicit, implicit, multigrid, and dual time-stepping schemes with efficient preconditioners. Additionally, we facilitate meshing and simulating complex geometries through a mesh-free immersed boundary technique. We detail the available documentation and the test cases included in the GitHub repository.

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Section: Turbulence Closure Modelsmentioning

confidence: 99%

HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

Ferrer¹,

Rubio²,

Ntoukas³

et al. 2022

Preprint

Self Cite

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“…Before continuing with the numerical experiments, as in other works [22,42,24,43,44], we perform a von Neumann analysis to characterise the SVV in the one-dimensional advection-diffusion equation with constant coefficients. This will allow us to better understand the dissipative behaviour of the SVV filtering technique at different scales, knowledge that we can use to understand the results we find in the posterior Navier-Stokes experiments in Sec.…”

Section: Linear Von Neumann Analysismentioning

confidence: 99%

An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models

Mateo-Gabín¹,

Manzanero²,

Valero³

2021

Preprint

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We present a stable spectral vanishing viscosity for discontinuous Galerkin schemes, with applications to turbulent and supersonic flows. The idea behind the SVV is to spatially filter the dissipative fluxes, such that it concentrates in higher wavenumbers, where the flow is typically under-resolved, leaving low wavenumbers dissipation-free. Moreover, we derive a stable approximation of the Guermond-Popov fluxes with the Bassi-Rebay 1 scheme, used to introduce density regularization in shock capturing simulations. This filtering uses a Cholesky decomposition of the fluxes that ensures the entropy stability of the scheme, which also includes a stable approximation of boundary conditions for adiabatic walls. For turbulent flows, we test the method with the three-dimensional Taylor-Green vortex and show that energy is correctly dissipated, and the scheme is stable when a kinetic energy preserving split-form is used in combination with a low dissipation Riemann solver. Finally, we test the shock capturing capabilities of our method with the Shu-Osher and the supersonic forward facing step cases, obtaining good results without spurious oscillations even with coarse meshes.

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Exploring the potential of TENO and WENO schemes for simulating under-resolved turbulent flows in the atmosphere using Euler equations

Navas-Montilla,

Guallart,

Solán-Fustero

et al. 2024

Computers & Fluids

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Application of approximate dispersion-diffusion analyses to under-resolved Burgers turbulence using high resolution WENO and UWC schemes

Cited by 11 publications

References 46 publications

HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models

Exploring the potential of TENO and WENO schemes for simulating under-resolved turbulent flows in the atmosphere using Euler equations

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