Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements

Kopriva, David A.; Hindenlang, Florian; Bolemann, Thomas; Gassner, Gregor J.

doi:10.1007/s10915-018-00897-9

Cited by 18 publications

(4 citation statements)

References 42 publications

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“…Additionally, the polynomial order can be different in each spatial dimension (P x , P y , P z ), allowing anisotropic p-adaptation. Treatment of the geometrical representation of the p-non-conforming faces for general curvilinear hexahedral elements is performed following the rules presented in [54]. The coupling between the faces of elements with different polynomial orders is performed using the mortar method [55], which does not retain entropy stability.…”

Section: Spatial P-adaptationmentioning

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: Spatial P-adaptationmentioning

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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“…Having a watertight mesh is a necessary condition but not sufficient. For free-stream preservation, the mesh has to satisfy two additional conditions [65],…”

Section: Continuous Free-energy Stabilitymentioning

confidence: 99%

A free–energy stable p–adaptive nodal discontinuous Galerkin for the Cahn–Hilliard equation

Ntoukas

Manzanero

Rubio

et al. 2021

Journal of Computational Physics

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A novel free-energy stable discontinuous Galerkin method is developed for the Cahn-Hilliard equation with non-conforming elements. This work focuses on dynamic polynomial adaption (p-refinement) and constitutes an extension of the method developed by Manzanero et al. in Journal of Computational Physics 403:109072, 2020, which makes use of the summation-by-parts simultaneous-approximation term technique along with Gauss-Lobatto points and the Bassi-Rebay 1 (BR1) scheme. The BR1 numerical flux accommodates nonconforming elements, which are connected through the mortar method. The scheme has been analytically proven to retain its free-energy stability when transitioning to non-conforming elements. Furthermore, a methodology to perform the adaption is introduced based on the knowledge of the location of the interface between phases. The adaption methodology is tested for its accuracy and effectiveness through a series of steady and unsteady test cases. We solve a steady one-dimensional interface test case to initially examine the accuracy of the adaption. Furthermore, we study the formation of a static bubble in two dimensions and verify that the accuracy of the solver is maintained while the degrees of freedom decrease to less than half compared to the uniform solution. Lastly, we examine an unsteady case such as the spinodal decomposition and show that the same results for the free-energy are recovered with a 35% reduction of the degrees of freedom for the two-dimensional case considered and a 48% reduction for the three-dimensional case.

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“…This suggestion has been proven to work perfectly on curved conforming meshes. A recent work [50] on curved nonconforming meshes in the special scenario of subdivision of parent element reveals that a necessary condition for freestream preservation is that the metrics of a child face being computed from its parent face. But for general curved nonconforming meshes, such as the sliding meshes in this work, a child face (e.g., a mortar) does not have a unique parent (more specifically, a child face has two parent faces that are different polynomials), and thus the aforementioned necessary condition generally can not be satisfied.…”

Section: Free-stream Preservationmentioning

confidence: 99%

A Conservative High-Order Method Utilizing Dynamic Transfinite Mortar Elements for Flow Simulation on Curved Sliding Meshes

Zhang,

Liang

2020

Preprint

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We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The method is arbitrarily high-order accurate in space, provably conservative, and satisfies outflow condition. Moreover, it retains the accuracy of a time marching scheme, and thus allows substantial reduction of rotational speed effects when equipped with a high-order temporal scheme. The method's capability of simultaneously handling multiple rotational objects is also explored. Details on the implementation are provided as well.

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Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements

Cited by 18 publications

References 42 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

A free–energy stable p–adaptive nodal discontinuous Galerkin for the Cahn–Hilliard equation

A Conservative High-Order Method Utilizing Dynamic Transfinite Mortar Elements for Flow Simulation on Curved Sliding Meshes

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