Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2005.13914

Projective Integration Schemes for Hyperbolic Moment Equations

Julian Koellermeier·Giovanni Samaey
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we apply projective integration methods to hyperbolic moment models of the Boltzmann equation and the BGK equation, and investigate the numerical properties of the resulting scheme. Projective integration is an explicit, asymptotic-preserving scheme that is tailored to problems with large spectral gaps between slow and (one or many) fast eigenvalue clusters of the model. The spectral analysis of a linearized moment model clearly shows spectral gaps and reveals the multi-scale nature of the model for which projective integration is a matching choice. The combination of the non-intrusive projective integration method with moment models allows for accurate, but efficient simulations with significant speedup, as demonstrated using several 1D and 2D test cases with different collision terms, collision frequencies and relaxation times.

Explore related subjects

physics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Julian Koellermeier, Giovanni Samaey. 2021-01-05. Projective Integration Schemes for Hyperbolic Moment Equations. https://arxiv.org/abs/2005.13914

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A subcell-refined entropy-residual-driven limiting strategy for high-order discontinuous Galerkin methods

Fine-grained, subcell-level dissipation control is essential for achieving robust high-order discontinuous Galerkin (DG) simulations of nonlinear hyperbolic systems in under-resolved regimes while preserving accuracy. This paper proposes a subcell-refined entropy-residual-driven limiting strategy for DG on Legendre-Gauss-Lobatto nodes. The limiter introduces only nearest-neighbor pairwise dissipation within each element, with closed-form coefficients that supply the minimal dissipation required to restore the element entropy inequality. The strategy is a diagonal, locally stable approximation of classical entropy-stable methods, and a generalized subcell framework reveals split-form DG and residual-distribution-based entropy correction schemes as particular choices of the limiting coefficients. For the Euler equations, a physically consistent jump operator separately models thermal and shear entropy production while preserving velocity and pressure equilibrium; a subcell refinement of the Zhang-Shu positivity limiter ensures pointwise positivity. Extensive numerical tests confirm that the scheme maintains optimal high-order accuracy, strictly enforces entropy dissipation, and significantly reduces the difficulty of a posteriori positivity-preserving procedures.

physics.comp-ph↗
arXiv2026

VNS Tokamak for Medical Isotope Production

The Volumetric Neutron Source (VNS) tokamak is a proposed fusion reactor for testing components under fusion neutron irradiation, and has potential use for radioisotope production. The VNS geometry is modeled in the Serpent 2.2.2 and OpenMC 0.15.2 neutronics codes. Coupled neutron-photon simulations compared fluxes, spectra, and selected reaction rates in the blanket and vacuum vessel. Good agreement was found overall, with the largest difference found in (n, 2n) reactions. On an HPC cluster, Serpent 2 was found to have shorter computation time in coupled simulations, while OpenMC was faster in neutron only simulations. Radioisotope production yields were simulated in Serpent 2.2.2 for capsule and Cobalt plate irradiation facilities. Results indicate potential for large volume production of 99Mo, 131I, 225Ac, 177Lu, 192Ir, 64Cu, 67Cu, 161Tb, and 153Sm while 203Pb indicates lower potential. 100Mo and LEU target heating was calculated, suggesting the LEU target mass or the cooling may need adjustment. Optimized 60Co production yielded 1.2 GBq/mg and 100,000 TBq after a 3-year irradiation period. Sensitivity to plant outage for 99Mo, 131I, 177Lu, and 60Co was simulated, suggesting irradiation can be restarted for the same isotope loading and demonstrated long-lived 60Co to be robust to long plant dwell-time.

physics.comp-ph↗
arXiv2026

MadVfold: accelerating NLO event generation and reducing negative weights with SIMD vectorization and GPUs

NLO simulations are essential for LHC physics analyses but are expensive, as they are not only slow but also lead to negative weights, which imply the need to simulate much larger samples of events. Folding is a powerful technique to reduce negative weights but is itself expensive. In this paper I propose ``vectorized folding'' as a new idea to speed up these calculations using SIMD and GPUs, and I present its CUDACPP-based implementation for MG5aMC in MadVfold, including its extension for unfolded NLO event generation. Preliminary results show overall speedups around 6x to 9x with folding and 3x without it. This work is based on a test-centric, LLM-assisted software development process.

physics.comp-ph↗