A shock-fitting technique for 2D unstructured grids

Paciorri, Renato; Bonfiglioli, Aldo

doi:10.1016/j.compfluid.2008.07.007

Cited by 72 publications

(73 citation statements)

References 43 publications

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“…The coupling of the shockfitting technique with a shock-capturing solver also enables a hybrid mode of operation in which some of the shocks are fitted, whereas all others are captured. The reader is referred to [23][24][25][26][27] for a detailed description of the two-, respectively three-dimensional, version of this novel unstructured shock-fitting approach; here we report some examples demonstrating how the advances in unstructured mesh generation enabled us to bring shock fitting back to life. …”

Section: Shock Fittingmentioning

confidence: 99%

“…Indeed, the two variations of the basic technique that have been so far proposed in the structured grid setting, that is, "boundary" shock fitting and "floating" shock fitting, are either algorithmically simple, but limited to topologically 3 simple configurations or more widely applicable, but algorithmically complex. Recently, a new shock-fitting technique for unstructured two-and three-dimensional meshes has been proposed and developed [23][24][25][26][27] by two of the authors of this article. This new technique reduces significantly the algorithmic difficulties encountered in the previous implementations of the shock-fitting technique within the structured-grid context.…”

Section: 4] For Details)mentioning

confidence: 99%

“…A thorough account of these difficulties can be found in [53]. Taking advantage of the availability of public domain software libraries [56][57][58][59][60] that accomplish unstructured, volumetric, and surface mesh generation, a novel unstructured shock-fitting technique that combines features of both the boundary and floating shock-fitting techniques has been recently developed by two of the authors [23][24][25][26][27]. In this novel unstructured shock-fitting approach the shock front is discretized as a double-sided, triangulated surface (a polygonal curve in 2D) which is treated as a zero-thickness, internal boundary by the shock-capturing eulfs [43,44] solver (whose main features have already been described in Section 2.3) which is used to discretize the governing PDEs within the computational domain.…”

Section: Shock Fittingmentioning

confidence: 99%

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The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

Bonfiglioli

Paciorri

Mascio

2012

Modelling and Simulation in Engineering

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Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

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Section: Shock Fittingmentioning

confidence: 99%

Section: 4] For Details)mentioning

confidence: 99%

Section: Shock Fittingmentioning

confidence: 99%

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The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

Bonfiglioli

Paciorri

Mascio

2012

Modelling and Simulation in Engineering

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“…It should be noted here that these methods do not resolve the internal structure of shocks. This method suffers from issues of accuracy, stability and quality, particularly for hypersonic simulations using unstructured grids [5]. Best practices dictate that shock-fitting should be used to model external and bow shocks, and shock-capturing should be used for internal or embedded shocks.…”

Section: Shock-capturing Methodsmentioning

confidence: 99%

“…This may cause a reduction in performance or overly conservative designs for scenarios where shock waves occur, such as for supersonic aircraft, within overexpanded nozzles, or spacecraft re-entering the atmosphere. For this reason, and due to the complexity of numerically approximating discontinuities, modelling of shocks has been and remains one of the most significant aspects of numerical simulations of compressible flows [5].…”

Section: Introductionmentioning

confidence: 99%

Investigation into the use of Walsh functions for solving flow with shocks

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Precise numerical modelling of fluid flow properties across the discontinuity of a shock wave is critical for accurate flow information behind the shock. This is of particular importance for spacecraft re-entering the Earth's atmosphere or supersonic and hypersonic aircraft, which all experience extreme temperature loading behind their associated shocks.Current shock modelling methods such as shock-fitting or shock-capturing either suffer from discretisation error of modelling the shock across finite cells, or are limited in the types and locations of shocks that they can be applied to.First proposed by P. A. Gnoffo, a global series solution using discontinuous Walsh functions that does not require explicit discretisation was investigated to gain understanding of the method and its strengths and limitations [1]. Walsh functions are a group of square shaped waves with varying numbers of segments and segment lengths based on the number of the Walsh function and the family to which they belong.Instead of discretising the domain into cells or nodes, the resulting series solution is made up of a number of scaled Walsh functions that are present across the full domain.The number of Walsh functions being used in this series solution must be truncated at some finite value, resulting in a form of "discretisation". Self-replicating properties under multiplication mean that the Walsh functions lend themselves well to series solutions; inherent discontinuities allow for highly accrute modelling of discontinuous functions.Following from Gnoffo's work, this thesis provides more user-friendly explanations of the fundamentals of Walsh functions regarding function representations. A derivation of the 1-dimensional heat equation is provided to offer a second example of setting up the system of algebraic equations, which can be solved numerically to find the solution to the heat equation. Furthermore, the global series solution approach for Burgers' equation has been explained in more detail, such that it could now be quite easily replicated. For each of these topics supporting code, which has been validated using visual inspection and error comparison, is provided to assist the reader in implementation. ii Acknowledgements First and foremost, this thesis could not have been completed without the assistance provided by my supervisor Dr. Rowan Gollan. You never failed to solve issues I would be hung up on for weeks or at least point me in the right direction. I also thank you warmly for making time to meet with me much more often than you would be expected in these past two weeks, and for accommodating me as I frantically attempted to pull together results towards the end of the semester.Thanks to the mech boys: Will, Damian, Matt, Ethan and Dave. Having a good group to go through my degree with over the past four years has been greatly appreciated.Also, thanks goes to my housemates for keeping me sane and fed in these past two weeks.And last but not least, thanks to my family for listening to my troubles, I appreciate ever...

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Unsteady shock‐fitting for unstructured grids

Bonfiglioli

Paciorri

Campoli

2015

Numerical Methods in Fluids

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An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has being further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows, the steady algorithm. The properties of the unsteady version of this novel, unstructured shock-fitting technique, are tested by reference to the inviscid interaction between a vortex and a planar shock: a comparative assessment of shock-capturing and shock-fitting is made for the same test problem

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A shock-fitting technique for 2D unstructured grids

Cited by 72 publications

References 43 publications

The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

Investigation into the use of Walsh functions for solving flow with shocks

Unsteady shock‐fitting for unstructured grids

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