A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

Uddin, Hasib; Kramer, Richard Michael Jack; Pantano, Carlos

doi:10.1016/j.jcp.2014.01.004

Cited by 34 publications

(17 citation statements)

References 90 publications

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“…The initial conditions are applied according to the exact solutions, Eqs. (46) and (47) at time t = 0. First let us consider the solution of this problem with the Dirichlet boundary conditions along all boundaries.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…There is a significant number of publications related to the numerical solution of different PDE on irregular domains with uniform embedded meshes. For example, we can mention the following fictitious domain numerical methods that use uniform embedded meshes: the embedded finite difference method, the cut finite element method, the finite cell method, the Cartesian grid method, the immersed interface method, the virtual boundary method, the embedded boundary method, etc; e.g., see [44,47,6,40,41,11,16,52,36,31,29,30,28,27,15,7,5,4,35,42,10,8,9,37,26,3,46,33,45,17] and many others. The main objective of these techniques is to simplify the mesh generation for irregular domains as well as to mitigate the effect of 'bad' elements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

Idesman¹

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

Idesman¹

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…One of the difficulties in extension to irregular geometries of a ghost-cell immersed boundary method's lies in how to track the boundaries correctly. To the best of our knowledge, two ways to overcome this exist: the unstructured triangle surface mesh (Gilmanov et al, 2003;Mittal et al, 2008;Nagendra et al, 2014) and the combination with level-set signed distance functions (Liu and Hu, 2014;Uddin et al, 2014). The first method can be used to represent arbitrary geometries and has gained its popularity in biological fluid mechanics.…”

Section: Complex Geometriesmentioning

confidence: 99%

Treatment of solid objects in the Pencil Code using an immersed boundary method and overset grids

Aarnes

Jin

Mao

et al. 2018

Geophysical & Astrophysical Fluid Dynamics

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Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical accuracy. We present here an investigation of the use of the different methods with the purpose of assessing their strengths and weaknesses. At present, the overset grid method in the Pencil Code can only be used for representing cylinders in the flow. For this task it surpasses the immersed boundary method in yielding highly accurate solutions at moderate computational costs. This is partly due to local grid stretching and a body-conformal grid, and partly due to the possibility of working with local time step restrictions on different grids. The immersed boundary method makes up the lack of computational efficiency with flexibility in regards to application to complex geometries, due to a recent extension of the method that allows our implementation of it to represent arbitrarily shaped objects in the flow.

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“…(73) converges to the same solution under refinement. The implementation of the method is a generalization of a recent implicit extension algorithm developed in [65], modified to ensure the idempotence of the extension operator; that is E 2 = E. First, a band of grid points that are within ∆ max = max(∆x, ∆y, ∆z) from the stoichiometric surface are identified as the boundary points ϕ bc (Dirichlet boundary condition data) of Eq. (73).…”

Section: The Extension Operatormentioning

confidence: 99%

A computational approach to flame hole dynamics using an embedded manifold approach

Knaus

Pantano

2015

Journal of Computational Physics

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We present a new numerical algorithm for tracking the evolution of flame holes in diffusion flames. The key element is the solution of an evolution equation for a flame state field defined on a complex moving surface. The surface itself can evolve in time and is defined implicitly as a level set of an associated Cartesian scalar field. The surface coordinates, or parameterization, do not need to be determined explicitly. Instead, the numerical method employs an embedding technique where the evolution equation is extended to the Cartesian space. In our application, the flame state field represents the chemical activity state of a diffusion flame; i.e. quenched and burning regions of the flame surface. We present a formulation that describes the formation, propagation, and growth of flames holes using edge-flame modeling in laminar and turbulent diffusion flames. The evolution equation is solved using a high-order finite-volume WENO method and a new extension algorithm defined in terms of propagation PDEs. The complete algorithm is demonstrated by tracking the dynamics of flame holes in a turbulent reacting shear layer and its applicability is also demonstrated in a turbulent reacting lifted jet simulation.

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A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

Cited by 34 publications

References 90 publications

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

Treatment of solid objects in the Pencil Code using an immersed boundary method and overset grids

A computational approach to flame hole dynamics using an embedded manifold approach

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