A Discontinuous Galerkin Coupled Wave Propagation/Circulation Model

Meixner, Jessica; Dietrich, J. C.; Dawson, Clint; Zijlema, Marcel; Holthuijsen, L.H.

doi:10.1007/s10915-013-9761-5

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…We remark that employing a unified DGFEM approximation in all dimensions has been utilised in other application areas, such as, for example, coupled wave/circulation problems, cf. [ 37 ]. Previous work using higher order local basis functions in angle has also aimed to build quadrature sets which decouple the angular variables, although the focus was on schemes where the angular quadrature is used in a collocation-type manner such as [ 25 , 32 , 33 ] for evaluating the angular integrals.…”

Section: Introductionmentioning

confidence: 99%

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport

Houston,

Hubbard,

Radley

et al. 2024

J Sci Comput

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We introduce an hp-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost identical form to standard multigroup discrete ordinates methods, meaning that solutions can be computed efficiently with high accuracy and in parallel within existing software. This method provides a unified discretisation of the space, angle, and energy domains of the underlying integro-differential equation and naturally incorporates both local mesh and local polynomial degree variation within each of these computational domains. Moreover, general polytopic elements can be handled by the method, enabling efficient discretisations of problems posed on complicated spatial geometries. We study the stability and hp-version a priori error analysis of the proposed method, by deriving suitable hp-approximation estimates together with a novel inf-sup bound. Numerical experiments highlighting the performance of the method for both polyenergetic and monoenergetic problems are presented.

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Section: Introductionmentioning

confidence: 99%