A Non‐Dissipative, Energy‐Conserving, Arbitrary High‐Order Numerical Method and Its Efficient Implementation for Incompressible Flow Simulation in Complex Geometries Article Swipe
Sreevatsa Anantharamu
,
Krishnan Mahesh
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1002/fld.5369
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1002/fld.5369
In the inviscid limit, the energy of a velocity field satisfying the incompressible Navier–Stokes equations is conserved. Non‐dissipative numerical methods that discretely mimic this energy conservation feature have been demonstrated in the literature to be extremely valuable for robust and accurate large‐eddy simulations of high Reynolds number incompressible turbulent flows. For complex geometries, such numerical methods have been traditionally developed using the finite volume framework and they have been at best second‐order accurate. This paper proposes a non‐dissipative and energy‐conserving numerical method that is arbitrary high‐order accurate for triangle/tetrahedral meshes along with its efficient implementation. The proposed method is a Hybridizable Discontinuous Galerkin (HDG) method. The crucial ingredients of the numerical method that lead to the discretely non‐dissipative and energy‐conserving features are: (i) The tangential velocity on the interior faces, just for the convective term, is set using the non‐dissipative central scheme and the normal velocity is enforced to be continuous, that is, (div)‐conforming. (ii) An exactly (pointwise) divergence‐free basis is used in each element of the mesh for the stability of the convective discretization. (iii) The combination of velocity, pressure, and velocity gradient spaces is carefully chosen to avoid using stabilization which would introduce numerical dissipation. The implementation description details our choice of the orthonormal and degree‐ordered basis for each quantity and the efficient local and global problem solution using them. Numerical experiments demonstrating the various features of the proposed method are presented. The features of this HDG method make it ideal for high‐order LES of incompressible flows in complex geometries.
Related Topics
Concepts
Discretization
Dissipative system
Discontinuous Galerkin method
Mathematics
Dissipation
Inviscid flow
Vector field
Numerical stability
Reynolds number
Numerical analysis
Applied mathematics
Mathematical analysis
Classical mechanics
Finite element method
Turbulence
Physics
Geometry
Mechanics
Thermodynamics
Quantum mechanics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1002/fld.5369
- OA Status
- hybrid
- References
- 35
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4405851798Canonical identifier for this work in OpenAlex
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https://doi.org/10.1002/fld.5369Digital Object Identifier
- Title
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A Non‐Dissipative, Energy‐Conserving, Arbitrary High‐Order Numerical Method and Its Efficient Implementation for Incompressible Flow Simulation in Complex GeometriesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-12-26Full publication date if available
- Authors
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Sreevatsa Anantharamu, Krishnan MaheshList of authors in order
- Landing page
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https://doi.org/10.1002/fld.5369Publisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1002/fld.5369Direct OA link when available
- Concepts
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Discretization, Dissipative system, Discontinuous Galerkin method, Mathematics, Dissipation, Inviscid flow, Vector field, Numerical stability, Reynolds number, Numerical analysis, Applied mathematics, Mathematical analysis, Classical mechanics, Finite element method, Turbulence, Physics, Geometry, Mechanics, Thermodynamics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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| referenced_works | https://openalex.org/W2025931426, https://openalex.org/W2078133941, https://openalex.org/W2022740560, https://openalex.org/W2161433140, https://openalex.org/W174580308, https://openalex.org/W1976562529, https://openalex.org/W2157822890, https://openalex.org/W2969262004, https://openalex.org/W209576205, https://openalex.org/W2051682834, https://openalex.org/W2318931849, https://openalex.org/W2666330546, https://openalex.org/W2376378314, https://openalex.org/W2014339952, https://openalex.org/W1988754720, https://openalex.org/W2410416051, https://openalex.org/W2937383268, https://openalex.org/W4205202801, https://openalex.org/W2963374982, https://openalex.org/W3126661955, https://openalex.org/W3083412230, https://openalex.org/W2554407892, https://openalex.org/W2206365535, https://openalex.org/W2051751432, https://openalex.org/W2148849010, https://openalex.org/W4246353874, https://openalex.org/W2001512608, https://openalex.org/W1966937952, https://openalex.org/W2520213077, https://openalex.org/W4283079468, https://openalex.org/W2021041911, https://openalex.org/W2085939266, https://openalex.org/W1970226611, https://openalex.org/W2480160909, https://openalex.org/W3139199651 |
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| corresponding_author_ids | https://openalex.org/A5069898553 |
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