An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

Sun, Hongwei; Darmofal, David L.

doi:10.1016/j.jcp.2014.08.035

Cited by 20 publications

(16 citation statements)

References 33 publications

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“…We first consider () and the viscous term in (), and follow the derivations in Sun and Darmofal for systems of elliptic equations. The primal formulation on each Ω ( i ) , i = 1,2, is found to be: find

u_{h}^{(i)} \in V_{h, p}^{(i)}

such that

\begin{matrix} \int_{Ω^{(i)}} \nabla u_{h}^{(i)} \cdot A^{(i)} \nabla v d Ω & + \int_{Γ^{(i)}} (〚 û^{(i)} - u_{h}^{(i)} 〛 \cdot {A^{(i)} \nabla v} - {{\hat{A σ}}^{(i)}} \cdot 〚 v 〛) d s \\ + \int_{Γ_{I}^{(i)}} ({û^{(i)} - u_{h}^{(i)}} 〚 A^{(i)} \nabla v 〛 - 〚 {\hat{A σ}}^{(i)} 〛 {v}) d s \\ + \int_{Σ} ((û^{(i)} - u_{h}^{(i)}) A^{(i)} \nabla v - {\hat{A σ}}^{(i)} v) \cdot {\hat{n}}^{(i)} d s \end{matrix}

…”

Section: Discontinuous Galerkin Methods For Conjugate Heat Transfer Prmentioning

confidence: 99%

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

Ojeda

Sun

Allmaras

et al. 2016

Numerical Meth Engineering

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Summary In this paper, we present a solution framework for high‐order discretizations of conjugate heat transfer problems on non‐body‐conforming meshes. The framework consists of and leverages recent developments in discontinuous Galerkin discretization, simplex cut‐cell techniques, and anisotropic output‐based adaptation. With the cut‐cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the discontinuous Galerkin discretization automatically adjusts the mesh in each sub‐domain and achieves high‐order accuracy in outputs of interest. We demonstrate the solution framework through several multi‐domained conjugate heat transfer problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be difficult to capture with user‐generated meshes. Copyright © 2016 John Wiley & Sons, Ltd.

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u_{h}^{(i)} \in V_{h, p}^{(i)}

such that

\begin{matrix} \int_{Ω^{(i)}} \nabla u_{h}^{(i)} \cdot A^{(i)} \nabla v d Ω & + \int_{Γ^{(i)}} (〚 û^{(i)} - u_{h}^{(i)} 〛 \cdot {A^{(i)} \nabla v} - {{\hat{A σ}}^{(i)}} \cdot 〚 v 〛) d s \\ + \int_{Γ_{I}^{(i)}} ({û^{(i)} - u_{h}^{(i)}} 〚 A^{(i)} \nabla v 〛 - 〚 {\hat{A σ}}^{(i)} 〛 {v}) d s \\ + \int_{Σ} ((û^{(i)} - u_{h}^{(i)}) A^{(i)} \nabla v - {\hat{A σ}}^{(i)} v) \cdot {\hat{n}}^{(i)} d s \end{matrix}

…”

Section: Discontinuous Galerkin Methods For Conjugate Heat Transfer Prmentioning

confidence: 99%

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

Ojeda

Sun

Allmaras

et al. 2016

Numerical Meth Engineering

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“…We first consider (1) and the viscous term in (2), and follow the derivations in Sun and Darmofal [17] for systems of elliptic equations. The primal formulation on each .i / ; i D 1; 2, is found to be: find…”

Section: Formulation Of the Discontinuous Galerkin Methodsmentioning

confidence: 99%

An Adaptive Simplex Cut-Cell Method for High-Order Discontinuous Galerkin Discretizations of Conjugate Heat Transfer Problems

Ojeda

Sun

Allmaras

et al. 2015

22nd AIAA Computational Fluid Dynamics Conference

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In this paper we present a PDE solution framework for high-order discretizations of conjugate heat transfer (CHT) problems on non-body-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an anisotropic output-based adaptive scheme. With the cut-cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the DG discretization automatically adjusts the mesh in each sub-domain and achieves high-order accuracy in outputs of interest, namely heat flux across an interface. We demonstrate our proposed framework through several multi-domained CHT problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be di cult to capture with user generated meshes. Our proposed automatic mesh generation and adaptation scheme o↵ers a hands-free capability allowing for streamlined solutions and physical insight to complex CHT problems.

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“…Hence, immersed methods and high-order accurate schemes appeared until recently to be intrinsically incompatible. Contrary to this perception, lately, a number of high-order immersed methods have been introduced mostly for the finite element method, [6][7][8][9][10][11][12] and a few for the discontinuous Galerkin, [13][14][15][16] finite volume, [17][18][19] and finite difference methods. 20,21 Evidently, the techniques for the finite element and discontinuous Galerkin methods must share a number of features due to their common origins.…”

Section: Introductionmentioning

confidence: 99%

An immersed discontinuous Galerkin method for compressible Navier‐Stokes equations on unstructured meshes

Hong

Febrianto

Zhang

et al. 2019

Numerical Methods in Fluids

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Summary We introduce an immersed high‐order discontinuous Galerkin method for solving the compressible Navier‐Stokes equations on non–boundary‐fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are advanced in time with an explicit time marching scheme. The discretisation meshes may contain simplicial (triangular or tetrahedral) elements of different sizes and need not be structured. On the discretisation mesh, the fluid domain boundary is represented with an implicit signed distance function. The cut‐elements partially covered by the solid domain are integrated after tessellation with the marching triangle or tetrahedra algorithms. Two alternative techniques are introduced to overcome the excessive stable time step restrictions imposed by cut‐elements. In the first approach, the cut‐basis functions are replaced with the extrapolated basis functions from the nearest largest element. In the second approach, the cut‐basis functions are simply scaled proportionally to the fraction of the cut‐element covered by the solid. To achieve high‐order accuracy, additional nodes are introduced on the element faces abutting the solid boundary. Subsequently, the faces are curved by projecting the introduced nodes to the boundary. The proposed approach is verified and validated with several two‐ and three‐dimensional subsonic and hypersonic low Reynolds number flow applications, including the flow over a cylinder, a space capsule, and an aerospace vehicle.

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An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

Cited by 20 publications

References 33 publications

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

An adaptive simplex cut‐cell method for high‐order discontinuous Galerkin discretizations of conjugate heat transfer problems

An Adaptive Simplex Cut-Cell Method for High-Order Discontinuous Galerkin Discretizations of Conjugate Heat Transfer Problems

An immersed discontinuous Galerkin method for compressible Navier‐Stokes equations on unstructured meshes

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