A High-Order Geometric-Compatible DGSEM with Subcell Limiting for the GPR System
Abstract
We construct an equation-of-state-independent geometric-compatible finite-volume (GC-FV) method and a high-order nodal discontinuous Galerkin spectral-element extension (GC-DG) for a reduced Godunov-Peshkov-Romenski system on fixed Eulerian meshes. Density is recovered from ρ=ρ0det(A), so mass conservation is a hidden companion law of the distortion equation. Starting from a straight-path Dal Maso-LeFloch-Murat fluctuation pair, minimum-change cofactor projections produce a single-valued density flux and exact induced local Lax-Friedrichs dissipation without jump quotients. The summation-by-parts property lifts the geometric two-state identity to high order and yields an equivalent subcell representation of GC-DG. We then blend GC-DG with the compatible GC-FV operator on the same Legendre-Gauss-Lobatto subcells. Because both operators induce the same boundary density flux, the global subcell blend retains the exact semidiscrete mass balance while suppressing shock-generated oscillations. A complementary modal/face-jump indicator supplies the elementwise blending coefficient. Numerical experiments verify high-order convergence, the expected temporal scaling of the fully discrete mass drift, and robust shock capturing for fluid, nonlinear-elastic, thermal-wave, and elastoplastic problems, including genuinely multidimensional configurations.
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BibTeX
@misc{yang2026highorder,
title = {{A High-Order Geometric-Compatible DGSEM with Subcell Limiting for the GPR System}},
author = {Jielin Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34755},
eprint = {2610.34755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34755},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A High-Order Geometric-Compatible DGSEM with Subcell Limiting for the GPR System
AU - Jielin Yang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34755
UR - https://arxiv.org/abs/2610.34755
AB - We construct an equation-of-state-independent geometric-compatible finite-volume (GC-FV) method and a high-order nodal discontinuous Galerkin spectral-element extension (GC-DG) for a reduced Godunov-Peshkov-Romenski system on fixed Eulerian meshes. Density is recovered from ρ=ρ_0det(A), so mass conservation is a hidden companion law of the distortion equation. Starting from a straight-path Dal Maso-LeFloch-Murat fluctuation pair, minimum-change cofactor projections produce a single-valued density flux and exact induced local Lax-Friedrichs dissipation without jump quotients. The summation-by-parts property lifts the geometric two-state identity to high order and yields an equivalent subcell representation of GC-DG. We then blend GC-DG with the compatible GC-FV operator on the same Legendre-Gauss-Lobatto subcells. Because both operators induce the same boundary density flux, the global subcell blend retains the exact semidiscrete mass balance while suppressing shock-generated oscillations. A complementary modal/face-jump indicator supplies the elementwise blending coefficient. Numerical experiments verify high-order convergence, the expected temporal scaling of the fully discrete mass drift, and robust shock capturing for fluid, nonlinear-elastic, thermal-wave, and elastoplastic problems, including genuinely multidimensional configurations.
ER -