Front-Tracking Methods

She, Dan; Kaufman, R. N.; Lim, Hyunkyung; Melvin, Jeremy; Hsu, Abigail; Glimm, James

doi:10.1016/bs.hna.2016.07.004

Cited by 14 publications

(10 citation statements)

References 35 publications

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“…In an attempt to avoid this issue, a number of techniques have been developed that instead track the motion of the interface explicitly. Front tracking methods, introduced in the works of Glimm et al and She et al and extended to DG in the work of Nguyen et al, are particularly well suited for tracking the evolution of material or contact discontinuities. Rather than requiring physical interfaces to be aligned with grid interfaces, the extended finite element method uses local enrichment functions to represent interfaces that require special quadrature rules to perform the numerical integration.…”

Section: Introductionmentioning

confidence: 99%

A moving discontinuous Galerkin finite element method for flows with interfaces

Corrigan

Kercher

Kessler

2018

Numerical Methods in Fluids

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Summary A moving discontinuous Galerkin finite element method with interface condition enforcement is formulated for flows with discontinuous interfaces. The underlying weak formulation enforces the interface condition separately from the conservation law, so that the residual only vanishes upon satisfaction of both. In this formulation, the discrete grid geometry is treated as a variable, so that, in contrast to the standard discontinuous Galerkin method, this method has both the means to detect interfaces, via interface condition enforcement, and to satisfy, via grid movement, the conservation law and its associated interface condition. The method therefore directly fits interfaces, including shocks, preserving a high‐order representation up to the interface without requiring shock capturing or an upwind numerical flux to achieve stability. It can be generalized to flows with a priori unknown interfaces with nontrivial topology and curved interface geometry as well as to an arbitrary number of spatial dimensions. Unsteady flows are represented in a manner similar to steady flows using a space‐time formulation. In addition to computing flows with interfaces, the method can represent point singularities in a flow field by degenerating cuboid elements. In general, the method works in conjunction with standard local grid operations, including edge collapse, to ensure that degenerate cells are removed. Test cases are presented for up to three‐dimensional flows that provide an initial assessment of the stability and accuracy of the method.

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Section: Introductionmentioning

confidence: 99%

A moving discontinuous Galerkin finite element method for flows with interfaces

Corrigan

Kercher

Kessler

2018

Numerical Methods in Fluids

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“…As already mentioned in the introduction, we refer to this new method as to extrapolated Shock-Tracking (eST) to differentiate it from unstructured shock fitting, in which a conformal mesh fitting the shock front is generated, and to differentiate it from the SBM, in which the true boundary is replaced by a unique surrogate with extrapolated boundary values. The eST method actually has similarities with high-order front tracking approaches [28], and also for this reason we prefer referring to it as shock-tracking. It may also be viewed as some sort of elaborate solution optimization procedure in which, starting from a captured result, one iteratively places the shock front and modifies the flow solution by solving the nonlinear jump conditions.…”

Section: Extrapolated Shock-trackingmentioning

confidence: 99%

“…the extension of the SBM to hyperbolic problems [27], the approach proposed here requires the solution of three coupled problems: the CFD upstream of the shock, the CFD downstream of the shock, the coupled algebraic system obtained from the Rankine-Hugoniot relations augmented with the characteristic information traveling toward the shock front. As in shock-fitting and front tracking methods [28], the shock front is explicitly discretized by an independent lower-dimensional mesh, and its position, as well as the position of the two surrogate boundaries, are themselves part of the computational result. These elements make the present work not only original w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Extrapolated Shock Tracking: Bridging shock-fitting and embedded boundary methods

Ciallella

Ricchiuto

Paciorri

et al. 2020

Journal of Computational Physics

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We propose a novel approach to approximate numerically shock waves. The method combines the unstructured shock-fitting approach developed in the last decade by some of the authors, with ideas coming from embedded boundary techniques. The numerical method obtained allows avoiding the remeshing phase required by the unstructured fitting method, while guaranteeing accuracy properties very close to those of the fitting approach. This new method has many similarities with front tracking approaches, and paves the way to shock-tracking techniques truly independent on the data and mesh structure used by the flow solver. The approach is tested on several problems showing accuracy properties very close to those of more expensive fitting methods, with a considerable gain in flexibility and generality.

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“…The purpose of this approach is eliminating the possibility of discontinuities in the thermal state, concentration, or thermodynamic phase that can result from the application of Eulerian advection methods. 10 However, two main challenges to the development and use of chemical kinetic models are present. The first challenge is the fact that various reactor models are needed for the modeling and simulation of different combustion problems.…”

Section: Introductionmentioning

confidence: 99%

Development of Reduced Chemical Kinetic Models for the Numerical Simulation of Combustion and Emissions Behavior of Representative Conventional and Bio-derived Fuels

Eldeeb¹

2020

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Front-Tracking Methods

Cited by 14 publications

References 35 publications

A moving discontinuous Galerkin finite element method for flows with interfaces

A moving discontinuous Galerkin finite element method for flows with interfaces

Extrapolated Shock Tracking: Bridging shock-fitting and embedded boundary methods

Development of Reduced Chemical Kinetic Models for the Numerical Simulation of Combustion and Emissions Behavior of Representative Conventional and Bio-derived Fuels

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