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Journal of Scientific Computing

Erschienen in:

01.06.2014

A Local Discontinuous Galerkin Method for the Propagation of Phase Transition in Solids and Fluids

verfasst von: Lulu Tian, Yan Xu, J. G. M. Kuerten, J. J. W. Van der Vegt

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2014

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Abstract

A local discontinuous Galerkin (LDG) finite element method for the solution of a hyperbolic–elliptic system modeling the propagation of phase transition in solids and fluids is presented. Viscosity and capillarity terms are added to select the physically relevant solution. The \(L^2-\)stability of the LDG method is proven for basis functions of arbitrary polynomial order. In addition, using a priori error analysis, we provide an error estimate for the LDG discretization of the phase transition model when the stress–strain relation is linear, assuming that the solution is sufficiently smooth and the system is hyperbolic. Also, results of a linear stability analysis to determine the time step are presented. To obtain a reference exact solution we solved a Riemann problem for a trilinear strain–stress relation using a kinetic relation to select the unique admissible solution. This exact solution contains both shocks and phase transitions. The LDG method is demonstrated by computing several model problems representing phase transition in solids and in fluids with a Van der Waals equation of state. The results show the convergence properties of the LDG method.

Vorheriger Artikel Superconvergence of Jacobi–Gauss-Type Spectral Interpolation

Nächster Artikel Energy Stable Flux Reconstruction Schemes for Advection–Diffusion Problems on Tetrahedra

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Titel: A Local Discontinuous Galerkin Method for the Propagation of Phase Transition in Solids and Fluids
verfasst von: Lulu Tian
Yan Xu
J. G. M. Kuerten
J. J. W. Van der Vegt
Publikationsdatum: 01.06.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9778-9

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